This paper presents a novel approach for distributed model predictive control (MPC) for piecewise affine (PWA) systems. Existing approaches rely on solving mixed-integer optimization problems, requiring significant computation power or time. We propose a distributed MPC scheme that requires solving only convex optimization problems. The key contribution is a novel method, based on the alternating direction method of multipliers, for solving the non-convex optimal control problem that arises due to the PWA dynamics. We present a distributed MPC scheme, leveraging this method, that explicitly accounts for the coupling between subsystems by reaching agreement on the values of coupled states. Stability and recursive feasibility are shown under additional assumptions on the underlying system. Two numerical examples are provided, in which the proposed controller is shown to significantly improve the CPU time and closed-loop performance over existing state-of-the-art approaches.

Uncertainty in the behavior of other traffic participants is a crucial factor in collision avoidance for automated driving; here, stochastic metrics could avoid overly conservative decisions. This article introduces a stochastic model predictive control (SMPC) planner for emergency collision avoidance in highway scenarios to proactively minimize collision risk while ensuring safety through chance constraints. To guarantee that the emergency trajectory can be attained, we incorporate nonlinear tire dynamics in the prediction model of the ego vehicle. Further, we exploit max-min-plus-scaling (MMPS) approximations of the nonlinearities to avoid conservatism, enforce proactive collision avoidance, and improve computational efficiency in terms of performance and speed. Consequently, our contributions include integrating a dynamic ego vehicle model into the SMPC planner, introducing the MMPS approximation for real-time implementation in emergency scenarios, and integrating SMPC with hybridized chance constraints and risk minimization. We evaluate our SMPC formulation in terms of proactivity and efficiency in various hazardous scenarios. Moreover, we demonstrate the effectiveness of our proposed approach by comparing it with a state-of-the-art SMPC planner and we validate that the generated trajectories can be attained using a high-fidelity vehicle model in IPG CarMaker.

This article proposes a framework for adaptive synchronization of uncertain underactuated Euler-Lagrange (EL) agents. The designed distributed controller can handle both state-dependent uncertain system dynamics terms and state-dependent uncertain interconnection terms among neighboring agents. No structural knowledge of such terms is required other than the standard properties of EL systems (positive definite mass matrix, bounded gravity, velocity-dependent friction bound, etc.). The study of stability relies on a suitable analysis of the nonactuated and the actuated synchronization errors, resulting in stable error dynamics perturbed by parametrized state-dependent uncertainty. This uncertainty is tackled via appropriate adaptation laws, giving stability in the uniform ultimate boundedness sense, in line with available literature on state-dependent uncertain system dynamics and/or state-dependent uncertain interconnections. An example with a network of boom cranes is used to validate the proposed approach.

Virtual coupling is regarded as an efficient way to improve the line capacity of rail transportation systems by reducing the spacing between consecutive trains. This paper is the first to compare and assess different distributed model predictive control (MPC) approaches, i.e., cooperative distributed MPC, serial distributed MPC, and decentralized MPC, for virtually coupled trains with a nonlinear train dynamic model. To make a balanced trade-off between computational complexity and efficiency, we also propose and assess convex approximations of the above control approaches. Furthermore, we are the first to introduce the relaxed dynamic programming approach to analyze the stability of the MPC-based nonlinear train control problem. By using the relaxed dynamic programming approach, a distributed stopping criterion with a stability guarantee is developed for the cooperative distributed MPC approach. In real life, masses of trains are different and can change at stations due to changes in passenger loads. This change in mass can significantly affect the dynamics and control of the virtually coupled trains when not taken into account in the control design. Therefore, we explicitly consider heterogeneous train masses when designing MPC approaches. We evaluate the different distributed MPC approaches through case studies based on the data of the Beijing Yizhuang Line. Simulation results indicate that the cooperative distributed MPC approach has the best tracking performance, while the serial distributed MPC approach can reduce communication requirements and computation capabilities with sacrifices of tracking performance.

Nonlinear Programs (NLPs) are prevalent in optimization-based control of nonlinear systems. Solving general NLPs is computationally expensive, necessitating the development of fast hardware or tractable suboptimal approximations. This paper investigates the sensitivity of the solutions of NLPs with polytopic constraints when the nonlinear continuous objective function is approximated by a PieceWise-Affine (PWA) counterpart. By leveraging perturbation analysis using a convex modulus, we derive guaranteed bounds on the distance between the optimal solution of the original polytopically-constrained NLP and that of its approximated formulation. Our approach aids in determining criteria for achieving desired solution bounds. Two case studies on the Eggholder function and nonlinear model predictive control of an inverted pendulum demonstrate the theoretical results.

Scenario reduction algorithms can be an effective means to provide a tractable description of the uncertainty in optimal control problems. However, they might significantly compromise the performance of the controlled system. In this paper, we propose a method to compensate for the effect of scenario reduction on stochastic optimal control problems for chance-constrained linear systems with additive uncertainty. We consider a setting in which the uncertainty has a discrete distribution, where the number of possible realizations is large. We then propose a reduction algorithm with a problem-dependent loss function, and we define sufficient conditions on the stochastic optimal control problem to ensure out-of-sample guarantees (i.e., against the original distribution of the uncertainty) for the controlled system in terms of performance and chance constraint satisfaction. Finally, we demonstrate the effectiveness of the approach on a numerical example.

The railway timetable rescheduling problem is regarded as an efficient way to handle disturbances. Typically, it is tackled using a mixed integer linear programming (MILP) formulation. In this paper, an algorithm that combines both reinforcement learning and optimization is proposed to solve the railway timetable rescheduling problem. Specifically, a value-based reinforcement learning algorithm is implemented to determine the independent integer variables of the MILP problem. Then, the values of all the integer variables can be derived from these independent integer variables. With the solution for the integer variables, the MILP problem can be transformed into a linear programming problem, which can be solved efficiently. The simulation results show that the proposed method can reduce passenger delays compared with the baseline, while also reducing the solution time.

This paper focuses on the development of linear Switched Box–Jenkins (SBJ) models for approximating complex dynamical models of biological wastewater treatment processes. We discuss the adaptation of these processes to the SBJ framework, showing the model's generality and flexibility as a class of switched systems that can offer accurate predictions for complex and nonlinear dynamics. This approach of modeling enables real-time data reconciliation from experiments and allows the design of model-based control strategies. Through the extension of the Outer Bounding Ellipsoids (OBEs) algorithm, the paper introduces an online two-stage parameter identification algorithm that effectively handles bounded disturbances for SBJ models. Using the OBE method relaxes the stochastic assumptions on disturbances, which may not be satisfied in practice, particularly for biological and environmental fluctuations. The proposed decomposed OBE algorithm separately identifies the switching patterns and parameters of linear submodels, conducting parameter identification in two distinct phases for input/output and disturbance/output submodels. The efficacy of this approach is shown via simulation results validated against both ADM1 and PBM models, demonstrating the proposed algorithm's capability to accurately predict outputs from different biological wastewater treatment models.

This paper proposes an approach to find the eigenvalues and eigenvectors of a class of autonomous max-min-plus-scaling (MMPS) systems. First we show that time invariant, monotone and non-expansive MMPS systems with only time variables has a unique structural eigenvalue and eigenvector under some conditions. Then, we propose a mixed integer linear programming (MILP) algorithm to calculate the eigenvalue and the corresponding eigenvector for such systems. Finally, we present a modified linear programming (LP) algorithm to find all the eigenvalues of a general time invariant MMPS system.

In this work we propose a new practical synchronization protocol for multiple Euler Lagrange (EL) systems without structural linear-in-the-parameters (LIP) knowledge of the uncertainty and where the agents can be interconnected before control design by unknown state-dependent interconnection terms. This setting is meant to overcome two standard a priori assumptions in the literature concerning uncertainty with LIP structure and absence of interaction among agents before designing the synchronization protocol. To overcome these assumptions, we propose an adaptive distributed control mechanism having the purpose of estimating the coefficients of the resulting state-dependent uncertainty structure.

In this paper, we discuss the stability of general time-invariant discrete-event systems modelled as max-min-plus-scaling (MMPS) systems. We analyze MMPS systems with two types of states: time states and quantity states. A set of linear programming problems are proposed to find the growth rates of the time states via a normalization of the MMPS system. Then a framework for stability analysis of the general time-invariant MMPS system is discussed with respect to the normalized system. The approach presented in this paper is an efficient way to study the stability of a general MMPS system.

Parameterized model predictive control (PMPC) is one of the many approaches that have been developed to alleviate the high computational requirement of model predictive control (MPC), and it has been shown to significantly reduce the computational complexity while providing comparable control performance with conventional MPC. However, PMPC methods still require a sufficiently accurate model to guarantee the control performance. To deal with model mismatches caused by the changing environment and by disturbances, this paper first proposes a novel framework that uses reinforcement learning (RL) to adapt all components of the PMPC scheme in an online way. More specifically, the novel framework integrates various strategies to adjust different components of PMPC (e.g., objective function, state-feedback control function, optimization settings, and system model), which results in a synthesis framework for RL-based adaptive PMPC. We show that existing adaptive (P)MPC approaches can also be embedded in this synthesis framework. The resulting combined RL-PMPC framework provides a solution for an efficient MPC approach that can deal with model mismatches. A case study is performed in which the framework is applied to freeway traffic control. Simulation results show that for the given case study the RL-based adaptive PMPC approach reduces computational complexity by 98% on average compared to conventional MPC while achieving better control performance than the other controllers, in the presence of model mismatches and disturbances.

In this paper, the disjunctive and conjunctive lattice piecewise affine (PWA) approximations of explicit linear model predictive control (MPC) are proposed. Training data consisting of states and corresponding affine control laws are generated in a control invariant set, and redundant sample points are removed to simplify the construction of lattice PWA approximations. Resampling is proposed to guarantee the equivalence of lattice PWA approximations and optimal MPC control law at the sample points. Under certain conditions, the disjunctive lattice PWA approximation constitutes a lower bound, while the conjunctive version formulates an upper bound of the original optimal control law. The equivalence of the two lattice PWA approximations then guarantees error-free approximations in the domain of interest, which is tested through a statistical guarantee. The performance of the proposed approximation strategy is tested through two simulation examples, and the results show that error-free lattice PWA approximations can be obtained with low offline complexity and small storage requirements. Besides, the online complexity is less compared with the state-of-the-art method.

In this article we consider the problem of tether entanglement for tethered mobile robots. One of the main risks of using a tethered connection between a mobile robot and an anchor point is that the tether may get entangled with the obstacles present in the environment or with itself. To avoid these situations, a non-entanglement constraint can be considered in the motion planning problem for tethered robots. This constraint is typically expressed as a set of specific tether configurations that must be avoided. However, the literature lacks a generally accepted definition of entanglement, with existing definitions being limited and partial in the sense that they only focus on specific instances of entanglement. In practice, this means that the existing definitions do not effectively cover all instances of tether entanglement. Our goal in this article is to bridge this gap and to provide new definitions of entanglement, which, together with the existing ones, can be effectively used to qualify the entanglement state of a tethered robot in diverse situations. The new definitions find application in motion planning for tethered robots, where they can be used to obtain more safe and robust entanglement-free trajectories.

Networks of dynamical systems play an important role in various domains and have motivated many studies on the control and analysis of linear dynamical networks. For linear network models considered in these studies, it is typically pre-determined what signal channels are inputs and what are outputs. These models do not capture the practical need to incorporate different experimental situations, where different selections of input and output channels are applied to the same network. Moreover, a unified view of different network models is lacking. This work makes an initial step towards addressing the above issues by taking a behavioral perspective, where input and output channels are not pre-determined. The focus of this work is on behavioral network models with only external variables. By exploiting the concept of hypergraphs, novel dual graphical representations, called system graphs and signal graphs, are introduced for behavioral networks. Moreover, connections between behavioral network models and structural vector autoregressive models are established. In addition to their connections in graphical representations, it is shown that the regularity of interconnections is an essential assumption when choosing a structural vector autoregressive model.

We consider the growth rate of a switching max-min-plus-scaling (S-MMPS) system in a discrete-event framework. We show that an explicit, time-invariant, monotone, and arbitrarily switching MMPS system has a bounded growth rate. Further, we propose a mixed-integer linear programming problem to calculate the estimates of the smallest upper bound and the largest lower bound of the growth rate of an S-MMPS system.

This paper presents a novel approach to multi-agent reinforcement learning (RL) for linear systems with convex polytopic constraints. Existing work on RL has demonstrated the use of model predictive control (MPC) as a function approximator for the policy and value functions. The current paper is the first work to extend this idea to the multi-agent setting. We propose the use of a distributed MPC scheme as a function approximator, with a structure allowing for distributed learning and deployment. We then show that Q-learning updates can be performed distributively without introducing nonstationarity, by reconstructing a centralized learning update. The effectiveness of the approach is demonstrated on a numerical example.

Humans and autonomous vehicles will jointly use the roads in smart cities. Therefore, it is a requirement for autonomous vehicles to properly handle the information and uncertainties that are introduced by humans (e.g., drivers, pedestrians, traffic managers) into the traffic, to accordingly make proper decisions. Such information is commonly available as linguistic, fuzzy (non-quantified) terms. Thus, we need mathematical modeling approaches that, at the same time, handle mixed (i.e., quantified and non-quantified) data. For this, we introduce novel type-2 sets and membership functions to translate such mixed traffic data into mathematical concepts that handle different levels and types of uncertainties and that can undergo mathematical operations. Next, we propose rule-based data processing and modeling approaches to exploit the advantages of these sets. This is inspired by the rule-based reasoning of humans, which has proven to be very effective and efficient in various applications, especially in traffic. The resulting models, hence, handle more than one level and type of uncertainty, which results in precise estimations of traffic dynamics that are comparable in accuracy with similar analyses if only one level of uncertainty (either probabilistic or fuzzy) would exist in the dataset. This will significantly improve the analysis, prediction, management, and safety of traffic in future smart cities.