Receding Horizon Control and Dissipativity - Optimal Control, Games and Uncertainty

I. Introduction

• MPC’s industrial success is linked to handling nonlinear, multi-input constrained systems and performance objectives, supported by efficient tailored optimization codes.The cited examples include convex and nonconvex optimization codes for implementation across hardware platforms.Source: §I · p. 1
• Dissipativity-based analysis of MPC emerged much later than the underlying theory, with turnpike behavior describing optimal trajectories that cluster near a stage-cost-optimal steady state.The introduction identifies early work linking turnpikes, dissipativity, and MPC as a basis for MPC analysis.Source: §I · p. 1
• Games suit non-cooperative agents pursuing their own outcomes; two-player zero-sum games yield min-max optimal control, and turnpike analysis spans deterministic and stochastic game settings.The introduction notes renewed work on stochastic zero-sum and non-zero-sum games and mean-field settings.Source: §I · pp. 1–2
• The paper frames four challenges: dissipativity in dynamic games, transfer of MPC analysis to receding-horizon games, stochastic decisions beyond Gaussian uncertainty, and algorithms for open-loop games.Rather than state exact theorems requiring detailed technical assumptions, it draws out common features and fundamental obstacles and points to formalizing literature.Source: §I · p. 2

II. Open-Loop Optimal Control and Games

• Optimization-based control is conceptually scalable from SISO to MIMO, but even convex linear-quadratic programs with linear inequalities can scale no better than O(N(nx ·nu)^3).The passage attributes this scaling to horizon length N and state and input dimensions nx and nu.Source: §II · p. 2
• Cooperative agents can be treated as one entity, whereas competitive open-loop games require distinct agent identities; control may instead use explicit feedback laws.The section introduces open-loop input sequences as an alternative to feedback and postpones the receding-horizon viewpoint to Section III.Source: §II · pp. 2–3

A. Optimal Control

• The optimal control formulation minimizes a finite-horizon objective over feasible state-input trajectories, with optimal solutions depending on the initial state and satisfying KKT conditions under mild differentiability assumptions.The exposition omits terminal penalties and constraints for simplicity, noting they can be added without conceptual difficulty.Source: A. Optimal Control · p. 3
• Dynamic programming offers an alternative: compute the optimal value function through the Bellman equation, then obtain the optimal one-step input, an approach connected to reinforcement learning.The passage also contrasts this with open-loop optimization, which yields primal trajectories and multiplier trajectories for each initial state.Source: A. Optimal Control · p. 3

• Agents’ costs, dynamics, or feasible actions can be coupled through shared dynamics, joint states and actions, or shared constraints; examples include autonomous driving, wireless networks, smart grids, and environmental games.Source: B. Open-Loop Games · p. 3
• The general game formulation can be specialized to local states or dynamics and to input-only or state-only cost and constraint coupling.Source: B. Open-Loop Games · p. 4
• Each agent optimizes its own problem while treating other agents’ actions as given, so game solutions need not coincide with solutions of the corresponding OCP.Source: B. Open-Loop Games · p. 4
• A generalized Nash equilibrium is a joint decision at which no agent can lower its cost by deviating unilaterally within its feasible actions, which may depend on other agents’ actions.Source: B. Open-Loop Games · p. 4
• Variational GNEs impose homogeneous multipliers across agents, making coupling-constraint marginal losses equal, and can be computed efficiently as variational inequalities using operator splitting.Source: B. Open-Loop Games · p. 4
• Under differentiability and convexity assumptions, the game yields per-agent KKT systems together with boundary conditions, primal feasibility, and complementary slackness.Source: B. Open-Loop Games · p. 4

C. Delineation of Games and OCPs

• Both OCP and GNEP trajectories approach a neighborhood of (xs, us) = (0, 0) mid-horizon before departing, while agents bear different input magnitudes in the game.The passages identify this as turnpike behavior for both problems; the open-loop trajectories are shown for N = 2, 4, 6, . . . , 18.Source: C. Delineation of Games and OCPs · p. 5, Figure 1 · p. 5

a) Objective gradients

• Games stack each agent’s objective gradient with respect to its own input into a pseudogradient, whose generally asymmetric Jacobian means it cannot usually be represented by a single OCP.In potential games, the pseudogradient integrates to a joint potential, yielding an OCP representation.Source: C. Delineation of Games and OCPs · p. 5

b) Constraints

• In a GNE, agents can have heterogeneous multipliers for coupled dynamics and inequalities; solutions coincide with an OCP only when these multipliers are shared, selecting a v-GNE.Different multipliers represent different agent burdens in satisfying constraints and, for resource allocation, heterogeneous shadow prices.Source: C. Delineation of Games and OCPs · p. 5

C. Delineation of Games and OCPs

• OCP solutions minimize the objective, whereas GNE solutions seek strategic equilibrium despite equivalent holistic-system feasible sets.The paper denotes these solutions with superscripts ⋄ and ∗, respectively.Source: C. Delineation of Games and OCPs · pp. 4–6

III. Receding Horizon Frameworks

• Repeatedly solving finite-horizon OCPs or GNEPs provides an alternative to computationally intractable infinite-horizon decision problems, except for specific structures such as linear systems with quadratic objectives.Explicit feedback via value functions is also subject to the curse of dimensionality outside specific settings.Source: §III · p. 6
• For OCPs and GNEPs, receding-horizon feedback is implicit: actions are obtained by solving a problem whose open-loop inputs depend on the initial state.The resulting closed-loop trajectories must be distinguished from the predicted trajectories computed during each optimization.Source: §III · p. 6

A. Model Predictive Control

• In deterministic setpoint stabilization, MPC’s history illustrates that optimality alone does not guarantee closed-loop stability.The passage describes early conceptualizations, process-industry applications in the 1970s, and later analysis of closed-loop properties.Source: A. Model Predictive Control · p. 6
• MPC stability can be fostered by designing the OCP so its infinite-horizon solutions match the task and its optimal value function serves as a Lyapunov candidate.The finite-horizon value function is also identified as a natural Lyapunov candidate, grounded in Bellman’s principle that optimal-solution tails are optimal.Source: A. Model Predictive Control · p. 7
• Terminal ingredients approximate the infinite-horizon value function, while relaxed dynamic programming bounds closed-loop performance when the suboptimality degree α lies in (0, 1].Under the relaxed-dynamic-programming approach, the prediction horizon N is the key tuning parameter for achieving the value-function approximation.Source: A. Model Predictive Control · p. 7
• With state and input constraints, recursive feasibility can be enforced through either terminal ingredients or sufficiently long prediction horizons.Recursive feasibility asks whether an initially feasible OCP remains feasible at every subsequent time.Source: A. Model Predictive Control · p. 7

B. Multi-Agent and Distributed MPC

• A multi-agent OCP optimizes the agents’ summed cost cooperatively, so solving it cooperatively to optimality retains the usual MPC stability discussion.The multi-agent structure is explicit, but the problem remains a single OCP.Source: B. Multi-Agent and Distributed MPC · p. 8
• Multi-agent OCPs support local control of many coordinated systems and distributed computation when problem size makes centralized implementation numerically intractable.Energy grids and cooperating robots are examples of interacting systems whose dynamics and constraints reflect interconnections.Source: B. Multi-Agent and Distributed MPC · p. 8
• Distributed algorithms approximate centralized solutions by exploiting interconnections, but their slower convergence makes interactions with inexact optimization relevant.Examples include ADMM and dual decomposition for linear dynamics and convex constraints, ALADIN and SQP-like methods for nonconvex problems, and neighboring-agent sensitivities or compatibility constraints to reduce computational burden,,,.Source: B. Multi-Agent and Distributed MPC · p. 8
• Distributed MPC cannot represent self-interested agents unwilling to cooperate, motivating the game-theoretic approach.A recent case study examined numerical scalability beyond 106 decision variables.Source: B. Multi-Agent and Distributed MPC · p. 8

C. Receding Horizon Games

• An RHG repeatedly solves a finite-horizon dynamic GNEP and applies its solution in receding-horizon fashion, producing an implicit feedback policy.A selection mechanism chooses a unique GNE and extracts agents’ first inputs when equilibria are not unique,,.Source: C. Receding Horizon Games · p. 8
• Without conditions guaranteeing a unique GNE, a selection or tie-break rule is needed, and its effect on closed-loop trajectories remains an open research topic.The same formal need for selection can arise in MPC when multiple optimal solutions exist.Source: C. Receding Horizon Games · p. 8
• RHG closed-loop attractors are steady-state GNEs: they are both dynamic steady states and one-step Nash equilibria where no agent wants to deviate unilaterally.For the example’s special case, the GNE–OCP steady-state difference vanishes for M = 1; cost coupling causes the difference for multiple agents because each agent disregards effects on others.Source: C. Receding Horizon Games · pp. 8–9
• In the nonlinear example, closed-loop RHG and OCP trajectories converge to their respective steady states, while RHG open-loop predictions exhibit the turnpike property.The example uses two agents with local dynamics and a horizon length of N = 12; trajectories are plotted in Figure 3.Source: C. Receding Horizon Games · p. 9

IV. Dissipativity and Turnpikes

• Dissipativity is introduced as an approach to analyzing OCPs, GNEPs, and their receding-horizon variants.This section follows the paper’s introduction of OCP and GNEP concepts and the receding-horizon perspective on both.Source: §IV · p. 9

A. The Perspective of Willems

• Willems motivated dissipativity as a generalization of Lyapunov functions to input-output systems, using storage functions and supply rates in a defining inequality.Although Willems considered non-negative storage functions, the results presented here require only lower boundedness.Source: A. The Perspective of Willems · p. 9
• Willems’ foundational 1972 paper treated continuous time, the first discrete-time extension was due to, and special issues survey dissipativity’s control applications,.The cited passage describes dissipativity concepts as ubiquitous in systems and control.Source: A. The Perspective of Willems · p. 9
• A free-end-time OCP computes available storage as the maximum storage extractable through dynamic operation from the initial state.The OCP uses the system dynamics and fixes the initial state to x.Source: A. The Perspective of Willems · p. 9
• A system is dissipative if and only if its available storage is finite, and available storage is bounded below by zero.The equivalence is established for storage functions bounded from below.Source: A. The Perspective of Willems · p. 10
• The argument can be restricted to selected trajectory classes, including those with state and input constraints; required supply also has an OCP and reachability characterization.The required-supply OCP uses a prescribed terminal constraint.Source: A. The Perspective of Willems · p. 10

• Using stage cost ℓ as the supply, dissipativity inequalities connect optimal-control trajectories to lower bounds on the value function and to the Bellman inequality.Source: B. Dissipativity with Stage Costs · p. 10
• Strict dissipativity makes (xs, us) the unique global minimizer of (21), generalizing strict convexity and relaxing the stage-cost lower bound to constrained steady states.Source: B. Dissipativity with Stage Costs · pp. 10–11
• System dissipativity must hold across feasible state-input pairs, whereas OCP dissipativity can be required only along optimal pairs and shaped through costs, terminal costs, and constraints.The OCP framing is less restrictive for nominal receding-horizon control, whose closed-loop inputs come from finite-horizon open-loop problems.Source: B. Dissipativity with Stage Costs · p. 11
• For GNEPs, strict dissipativity of the aggregated cost as a system property is highly restrictive because the proposed inequality cannot hold over the OCP feasible set and would constrain all steady states.Source: B. Dissipativity with Stage Costs · p. 11
• The proposed GNEP route is OCP-level strict dissipativity around the game equilibrium, with strictness required along GNEP-generated trajectories; available storage and an Insight 4 counterpart extend to GNEPs.Source: B. Dissipativity with Stage Costs · p. 11

C. The Turnpike Phenomenon

• Across examples, optimal and GNE solutions from different initial conditions and horizon lengths approach a common steady-state neighborhood, spending longer near it as the horizon grows.Figure 4 provides an illustrative sketch of this behavior.Source: C. The Turnpike Phenomenon · p. 11

Turnpikes in OCPs:

• In OCPs, strict dissipativity implies a turnpike property when suitable reachability holds and the storage is bounded.The result is stated for optimal solutions.Source: Turnpikes in OCPs · p. 11
• The stated bound uses C(x), which does not depend on the horizon length N.This horizon independence appears in the OCP turnpike result.Source: Turnpikes in OCPs · p. 11
• Turnpike duration can be quantified by time spent outside a neighborhood, yielding cardinality turnpikes in discrete time and measure turnpikes in continuous time.Equivalently, one may measure time close to rather than far from the turnpike.Source: Turnpikes in OCPs · p. 12
• An alternative formalization bounds the distance of optimal state-input pairs from the turnpike by exponential terms in k and N−k.The cited bound has the form C(e^−ck − e^−c(N−k)), with C, c > 0.Source: Turnpikes in OCPs · p. 12
• Turnpike properties have been studied in games since the 1980s, with recent work spanning stochastic LQ and mean field games,, [28],,,.The section also notes dynamic GNE turnpikes in competitive supply chains.Source: Turnpikes in GNEPs · p. 12

Turnpikes in GNEPs:

• Work [57] first established an overarching GNEP turnpike theory for nonlinear costs, nonlinear constraints, and discrete-time dynamics.The paper notes that a system-theoretic formalization aligned with optimal-control characterizations had been missing.Source: Turnpikes in GNEPs · p. 12
• Bounded price of anarchy is the additional ingredient for extending OCP turnpike results to GNEPs [57]; it measures the worst GNEP solution’s aggregated-cost loss against the OCP solution,.The comparison uses the same stage cost and requires a finite OCP value.Source: Turnpikes in GNEPs · p. 12
• Under strict dissipativity, if suitable reachability holds and storage and price of anarchy are bounded, then all GNEP solutions satisfy the turnpike property [57, Thm. 3].Source: Turnpikes in GNEPs · p. 12
• Turnpike results can also be established through saddle-point optimality systems, while converse turnpike-to-dissipativity results have been studied for discrete-time and continuous-time OCPs and transferred to GNEPs,,, [57].Source: Turnpikes in GNEPs · p. 12

A. Model Predictive Control

• Economic MPC work uses terminal constraints and strict-dissipativity variants,, while studies settings without terminal ingredients and provides performance bounds.Source: A. Model Predictive Control · p. 12
• Infinite-horizon optimal trajectories converge to the turnpike steady state when the OCP solutions satisfy strict dissipativity.The dissipativity-based MPC analysis also relates finite-horizon optimal trajectories and storage to closed-loop properties.Source: A. Model Predictive Control · p. 13
• The value function plus storage provides a candidate Lyapunov function for practical asymptotic stability, and their gradients relate to the dynamics’ Lagrange multipliers.For sufficiently large horizons, the value-function gradient is closely related to the storage gradient; rotated stage costs are also relevant,, [67, Chap. 8].Source: A. Model Predictive Control · p. 13
• When open-loop optimal solutions have a turnpike leaving arc, closed-loop asymptotic stability at the steady state may fail, leaving stability of a horizon-dependent neighborhood,.The leaving-arc mechanisms are discussed in.Source: A. Model Predictive Control · p. 13

B. Receding Horizon Games

• Potential games reduce to centralized OCPs [89], while non-potential RHG stability results use restrictive pseudogradient dissipativity 8; LQ games also have open-loop and feedback Nash stability results.Source: B. Receding Horizon Games · p. 13
• For sufficiently large horizons, nonlinear GNEPs are recursively feasible without terminal constraints when continuity, compactness, controllability, bounded price of anarchy and storage, and stage dissipativity conditions hold.Source: B. Receding Horizon Games · p. 13
• Under Insight 10 conditions and a local bound on W, closed-loop RHG achieves practical asymptotic convergence for sufficiently large horizons.Source: B. Receding Horizon Games · p. 13
• Practical asymptotic stability follows if W has an upper bound in the RHG setting, but verifying that bound remains an open research topic [38, Prop. 1].Source: B. Receding Horizon Games · p. 13

VI. Uncertainty in OCPs

• Stochastic MPC replaces deterministic prediction with an SOCP; random stage costs require aggregation, commonly by expectation or risk measures such as CVaR.Source: §VI · p. 14
• Stochastic constraints can be enforced almost surely or probabilistically, but almost-sure formulations may be overly conservative or infeasible under unbounded disturbances.Source: §VI · pp. 14–15
• Lifting dynamics to random-variable space accommodates i.i.d. disturbances and random initial conditions, yielding time-varying predictions that support transfer of deterministic time-varying control techniques.Source: §VI · p. 14
• Nonanticipativity requires controls to depend only on information observable through the current state, equivalently representing them as deterministic feedback policies.Source: §VI · p. 15

A. The Stochastic Turnpike Property

• Earlier stochastic turnpike work focused on probability laws or moments,,, while newer results report sample-path phenomena,,.The distributional viewpoint allows the SOCP to be reformulated as a time-invariant Markov decision process, with invariant distributions serving as the equilibrium analogue.Source: A. The Stochastic Turnpike Property · p. 15
• For N=50, optimal-state PDFs show entry and exit transients around an approximately constant middle, indicating a distributional turnpike.The example uses uniformly distributed disturbances, showing that the dissipativity approach is not restricted to Gaussian settings.Source: A. The Stochastic Turnpike Property · p. 15, Figure 5 · p. 15
• Under the same disturbance realization, optimal-state trajectories remain close across prediction horizons for most of the horizon, indicating a pathwise turnpike.This pathwise behavior implies that the turnpike on the random-variable layer is time-varying, unlike the stationary distribution on the distributional layer.Source: A. The Stochastic Turnpike Property · p. 15, Figure 6 · p. 16
• A unified turnpike object is a time-varying stochastic process with a time-invariant distribution that realizes the law while satisfying system dynamics.Unlike an invariant distribution alone, this structure enables comparison of individual realization paths driven by the same disturbance sequence.Source: A. The Stochastic Turnpike Property · pp. 15–16
• Different pseudometrics define turnpikes by distance to the stationary process, including mean-square, Wasserstein distributional, and first-moment notions.These choices yield turnpike properties with differing strength and interpretation.Source: A. The Stochastic Turnpike Property · p. 16

B. Dissipativity for Stochastic OCPs

• Stochastic dissipativity has been extended from probability distributions and measures to random variables,, aligning its formulation with pathwise stochastic turnpike analysis.On random variables, the dissipation inequality and storage function are time-dependent, and the pseudometric determines which deviations from the stationary process are captured.Source: B. Dissipativity for Stochastic OCPs · p. 16
• In stochastic OCPs, strict dissipativity implies a stochastic turnpike when a suitable stochastic reachability condition holds, with both properties formulated using the same pseudometric d.This is the stochastic counterpart of the deterministic implication; compatibility of the pseudometric is key to relating the properties.Source: B. Dissipativity for Stochastic OCPs · pp. 16–17

C. Closed-Loop Results

• Stochastic closed-loop results remain less developed than deterministic theory; dissipativity- and turnpike-based analyses derive guarantees from SOCP structure, alongside approaches using robust-control concepts, terminal ingredients, and chance-constraint techniques.The structural approaches seek to transfer part of the deterministic link between dissipativity, turnpike properties, and MPC performance to stochastic settings,.Source: C. Closed-Loop Results · p. 17
• Strict stochastic dissipativity and a stochastic turnpike property, with suitable regularity, yield semi-global practical asymptotic stability and approximate overtaking and averaged near-optimality for stochastic MPC.The guarantees assume both properties hold with respect to a pseudometric d, and that auxiliary optimal value functions and the storage function satisfy suitable continuity and regularity conditions.Source: C. Closed-Loop Results · p. 17
• As prediction horizon N increases, the stability neighborhood and performance error decrease, vanishing in the infinite-horizon limit and recovering convergence and optimality.For every feasible initial condition, a sufficiently large horizon brings the closed loop toward the stationary process; overtaking suboptimality and averaged-performance error likewise vanish as N →∞.Source: C. Closed-Loop Results · p. 17
• With almost-sure constraints and expectation as the criterion, a pathwise dynamic programming principle makes full-information MPC coincide almost surely with MPC using pathwise measurements [131].In this simplified setting, control for a random initial state can be found by minimizing separately for each realization.Source: C. Closed-Loop Results · p. 18
• With risk measures or probabilistic constraints, that equivalence can fail: implementable MPC may incur extra errors or require conservative constraint handling, leaving transient performance suboptimal and implementability an open direction.Full distributional information is typically needed to verify probabilistic constraints, although partial-information schemes can guarantee closed-loop constraint satisfaction,,,,; dissipativity-based arguments can still ensure near-optimal averaged performance [145].Source: C. Closed-Loop Results · p. 18
• For prediction horizons N = 3, 4, 5, closed-loop state CDFs at time k = 150 approach the stationary distribution as N increases; sample paths approach its support, and cumulative and averaged costs improve.Source: C. Closed-Loop Results · p. 18

A. Numerical Optimal Control

• Open-source optimal-control tools support real-time MPC except in extremely large-dimensional settings; OSQP scales well to QPs with more than 106 decision variables,.The section cites,, and as examples of available tools.Source: A. Numerical Optimal Control · p. 19

B. Numerical Methods for Generalized Nash Equilibria

• General GNEPs are difficult quasi-variational inequalities with few solvers and limited or no convergence guarantees, motivating the focus on variational GNEs.Source: B. Numerical Methods for Generalized… · p. 19
• For linear-quadratic dynamic games, the finite-horizon GNEP becomes a monotone affine variational inequality, strongly monotone when λmin(Rv) is sufficiently large [37, Prop. 2].Source: B. Numerical Methods for Generalized… · p. 19
• Asymmetric Riccati–Stein solutions make the AVI operator asymmetric, so no finite-horizon game in the original state space has an OLNE corresponding to an infinite-horizon OLNE.Source: B. Numerical Methods for Generalized… · p. 19
• With a strongly monotone affine operator and a nonempty polyhedral feasible set for stacked state-input constraints, the AVI has a unique solution [151, Thm. 2.3.3].Source: B. Numerical Methods for Generalized… · p. 19

C. Douglas–Rachford Algorithms for AVIs

• Under the stated splitting assumptions, the Douglas–Rachford step is a quadratic program and converges globally, linearly under strong monotonicity, to the unique AVI solution.The step is an optimization problem because H + M1 is symmetric and the feasible set C is polyhedral.Source: C. Douglas–Rachford Algorithms for AVIs · p. 20
• For symmetric M and step λ = 1/2, the [153] design resembles a full step toward the unconstrained solution projected onto the constraint set C.The passage describes the resulting iteration as an optimization-based projection when ε is close to zero.Source: C. Douglas–Rachford Algorithms for AVIs · p. 20

D. Smoothing Newton Algorithms for AVIs

• Smoothing the Fischer–Burmeister function yields a differentiable KKT system with nonsingular Newton equations and local superlinear convergence; experiments report faster convergence and lower computation time than FB and DR methods [154].A linesearch can guarantee global convergence, and the previous sampling instant's equilibrium provides a natural warm start; the methods are centralized by construction.Source: D. Smoothing Newton Algorithms for AVIs · p. 20

VIII. Open Problems and Conclusions

• The overview compares dissipativity-based optimal-control and game approaches, considers non-Gaussian uncertainty and tailored numerical methods, and identifies open problems.Its conclusion presents dissipativity and the turnpike property as a unifying thread across open-loop OCPs, GNEPs, and their receding-horizon counterparts.Source: §VIII · p. 20

A. Open Problems

• RHG stability analysis remains young, with open needs for terminal ingredients, Lyapunov functions, equilibrium tracking, and guarantees under model mismatch, forecast errors, noise, and disturbances.Non-unique equilibria in nonlinear RHGs can cause discontinuous jumps in the feedback law; existing stability analyses assume perfect models and forecasts.Source: Deterministic receding horizon games · pp. 20–21

Deterministic receding horizon games:

• Constrained open-loop and receding-horizon stochastic games remain nascent, with non-Gaussian disturbances, risk-sensitive or distributionally robust objectives, and feasibility, stability, and performance guarantees still to be studied.Unconstrained stochastic LQ games have established OLNE and FNE characterizations through stochastic dynamic programming and coupled Riccati–Stein equations [155].Source: Stochastic receding horizon games · p. 21

Stochastic receding horizon games:

• A key stochastic MPC gap is that turnpike and dissipativity analyses use random variables or distributions, while practical controllers typically observe states.Extending theory to more general information structures remains an open problem.Source: Stochastic model predictive control · p. 21

Stochastic model predictive control:

• Exact stochastic OCP solutions are difficult for nonlinear systems, so whether turnpikes persist under policy or scenario approximations and how to analyze their suboptimality remain open questions.Numerical methods for stochastic OCPs have advanced, including work cited as.Source: Stochastic model predictive control · p. 21

Numerical methods:

• Dynamic-game numerical methods lag OCP/MPC counterparts, requiring real-time progress and exploration of distributed nonconvex-control and complementarity-constrained methods beyond Douglas–Rachford splitting,, [156].The cited alternatives may help push the frontiers of numerical game-theoretic methods.Source: Numerical methods · p. 21

B. Conclusions

• The tutorial surveys deterministic, stochastic, multi-agent, and game-theoretic receding-horizon control, contrasting OCP minimizers with generalized Nash equilibria in cost and constraint handling.It identifies dissipativity and the turnpike property as a unifying backbone and presents the overview as a starting point for further research.Source: B. Conclusions · p. 22