Manfred Morari

We propose a robust model predictive control (MPC) method for discrete-time linear systems with polytopic model uncertainty and additive disturbances. Optimizing over linear time-varying (LTV) state feedback controllers has been successfully used for robust MPC when only additive disturbances are present. However, it is challenging to design LTV state feedback controllers in the face of model uncertainty whose effects are difficult to bound. To address this issue, we propose a novel approach to over-approximate the effects of both model uncertainty and additive disturbances by a filtered additive disturbance signal. Using the System Level Synthesis framework, we jointly search for robust LTV state feedback controllers and the bounds on the effects of uncertainty online, which allows us to reduce the conservatism and minimize an upper bound on the worst-case cost in robust MPC. We provide a comprehensive …

Neural networks are known to be vulnerable to adversarial attacks, which are small, imperceptible perturbations that can significantly alter the network’s output. Conversely, there may exist large, meaningful perturbations that do not affect the network’s decision (excessive invariance). In our research, we investigate this latter phenomenon in two contexts:(a) discrete-time dynamical system identification, and (b) the calibration of a neural network’s output to that of another network. We examine noninvertibility through the lens of mathematical optimization, where the global solution measures the “safety" of the network predictions by their distance from the non-invertibility boundary. We formulate mixed-integer programs (MIPs) for ReLU networks and norms () that apply to neural network approximators of dynamical systems. We also discuss how our findings can be useful for invertibility certification in transformations between neural networks, eg between different levels of network pruning.

Index of Papers Published in the IEEE ACC 2023 Page 1 Index of papers published in the IEEE Control Systems Letters and presented at the American Control Conference (ACC 2023). In order of publication 2023: Volume 7 On the Emergent Hypocycloidal and Epicycloidal Formations in a Swarm of Double Integrator Agents G. Fedele and L. D’Alfonso IEEE Control Systems Letters Year: 2023, Volume: 7 Pages: 613-618, DOI: 10.1109/LCSYS.2022.3210044 Combined Left and Right Temporal Robustness for Control Under STL Specifications A. Rodionova, L. Lindemann, M. Morari and GJ Pappas IEEE Control Systems Letters Year: 2023, Volume: 7 Pages: 619-624, DOI: 10.1109/LCSYS.2022.3209928 Inverse Matrix Games With Unique Quantal Response Equilibrium Y. Yu, J. Salfity, D. Fridovich-Keil and U. Topcu IEEE Control Systems Letters Year: 2023, Volume: 7 Pages: 643-648, DOI: 10.1109/LCSYS.…

This work presents an explicit–implicit procedure to compute a model predictive control (MPC) law with guarantees on recursive feasibility and asymptotic stability. The approach combines an offline-trained fully-connected neural network with an online primal active set solver. The neural network provides a control input initialization while the primal active set method ensures recursive feasibility and asymptotic stability. The neural network is trained with a primal–dual loss function, aiming to generate control sequences that are primal feasible and meet a desired level of suboptimality. Since the neural network alone does not guarantee constraint satisfaction, its output is used to warm start the primal active set method online. We demonstrate that this approach scales to large problems with thousands of optimization variables, which are challenging for current approaches. Our method achieves a 2× reduction in online …

We study the temporal robustness of temporal logic specifications and show how to design temporally robust control laws for time-critical control systems. This topic is of particular interest in connected systems and interleaving processes such as multi-robot and human-robot systems where uncertainty in the behavior of individual agents and humans can induce timing uncertainty. Despite the importance of time-critical systems, temporal robustness of temporal logic specifications has not been studied, especially from a control design point of view. We define synchronous and asynchronous temporal robustness and show that these notions quantify the robustness with respect to synchronous and asynchronous time shifts in the predicates of the temporal logic specification. It is further shown that the synchronous temporal robustness upper bounds the asynchronous temporal robustness. We then study the control …

George's contributions in process design began with his Ph. D. thesis work which solved classical multistage process design optimization problems with non-convex structure using Lagrangian decomposition (Stephanopoulos and Westerberg, 1975). This required resolving the dual gap whilst preserving the separability of the subproblems, accomplished through the method of Hestenes. The problems of process optimization are important, but without effective process synthesis strategies, even the best

Many modern autonomous systems, particularly multi-agent systems, are time-critical and need to be robust against timing uncertainties. Previous works have studied left and right time robustness of signal temporal logic specifications by considering time shifts in the predicates that are either only to the left or only to the right. We propose a combined notion of temporal robustness which simultaneously considers left and right time shifts. For instance, in a scenario where a robot plans a trajectory around a pedestrian, this combined notion can now capture uncertainty of the pedestrian arriving earlier or later than anticipated. We first derive desirable properties of this new notion with respect to left and right time shifts and then design control laws for linear systems that maximize temporal robustness using mixed-integer linear programming. Finally, we present two case studies to illustrate how the proposed temporal …

In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regret of the online learning of the Linear Quadratic Regulator (LQR). Prior results state that the statistical difficulty for both benchmarks scales polynomially with the system state dimension up to system-theoretic quantities. However, this does not reveal the whole picture. By utilizing minimax lower bounds for both benchmarks, we prove that there exist non-trivial classes of systems for which learning complexity scales dramatically, ie exponentially, with the system dimension. This situation arises in the case of underactuated systems, ie systems with fewer inputs than states. Such systems are structurally difficult to control and their system theoretic quantities can scale exponentially with the system dimension dominating learning complexity. Under some additional structural assumptions (bounding systems away from uncontrollability), we provide qualitatively matching upper bounds. We prove that learning complexity can be at most exponential with the controllability index of the system, that is the degree of underactuation.