arXiv subjects

Manfred Morari

Publications and source records attributed to Manfred Morari.

At least 19 recordsLinked to original sources

arXiv2026

The Fragility of Learning LQG Controllers

Learning methods are increasingly used to synthesize controllers from data, yet existing sample-complexity characterizations for continuous control are sharp only in the fully observed setting. This paper studies the partially observed case by deriving information-theoretic lower bounds for learning Linear Quadratic Gaussian (LQG) controllers from offline trajectories generated by a (linear) exploration policy. We prove an $\varepsilon$-local minimax excess-cost lower bound that applies to any algorithm mapping the offline dataset to a stabilizing linear controller. The bound is expressed in terms of the Hessian of the LQG cost with respect to model parameters and the inverse Fisher Information induced by the exploration policy. We further provide system-theoretic characterizations of these objects, enabling transparent construction of hard instances. Instantiating the bound on classical fragile robust-control examples, including variants of the Doyle LQG fragility counterexample and non-minimum-phase systems, demonstrates when fragile robust control problems translate into high sample complexity for learning-enabled control. These results suggest the asymptotic optimality of certainty-equivalent synthesis and motivate the importance of both task-directed experiment design and system co-design for sample-efficient learning in partially observed control.

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arXiv2025

A Data-driven Predictive Control Architecture for Train Thermal Energy Management

We aim to improve the energy efficiency of train climate control architectures, with a focus on a specific class of regional trains operating throughout Switzerland, especially in Zurich and Geneva. Heating, Ventilation, and Air Conditioning (HVAC) systems represent the second largest energy consumer in these trains after traction. The current architecture comprises a high-level rule-based controller and a low-level tracking controller. To improve train energy efficiency, we propose adding a middle data-driven predictive control layer aimed at minimizing HVAC energy consumption while maintaining passenger comfort. The scheme incorporates a multistep prediction model developed using real-world data collected from a limited number of train coaches. To validate the effectiveness of the proposed architecture, we conduct multiple experiments on a separate set of train coaches; our results suggest energy savings between 10% and 35% with respect to the current architecture.

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arXiv2025

Layered Multirate Control of Constrained Linear Systems

Layered control architectures have been a standard paradigm for efficiently managing complex constrained systems. A typical architecture consists of: i) a higher layer, where a low-frequency planner controls a simple model of the system, and ii) a lower layer, where a high-frequency tracking controller guides a detailed model of the system toward the output of the higher-layer model. A fundamental problem in this layered architecture is the design of planners and tracking controllers that guarantee both higher- and lower-layer system constraints are satisfied. Toward addressing this problem, we introduce a principled approach for layered multirate control of linear systems subject to output and input constraints. Inspired by discrete-time simulation functions, we propose a streamlined control design that guarantees the lower-layer system tracks the output of the higher-layer system with computable precision. Using this design, we derive conditions and present a method for propagating the constraints of the lower-layer system to the higher-layer system. The propagated constraints are integrated into the design of an arbitrary planner that can handle higher-layer system constraints. Our framework ensures that the output constraints of the lower-layer system are satisfied at all high-level time steps, while respecting its input constraints at all low-level time steps. We apply our approach in a scenario of motion planning, highlighting its critical role in ensuring collision avoidance.

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arXiv2023

Combined Left and Right Temporal Robustness for Control under STL Specifications

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 robustness accounts for timing uncertainties.

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arXiv2023

Certified Invertibility in Neural Networks via Mixed-Integer Programming

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 $L_p$ norms ($p=1,2,\infty$) 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, e.g. between different levels of network pruning.

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arXiv2022

A note on the control of processes exhibiting input multiplicity

Steady state multiplicity can occur in nonlinear systems, and this presents challenges to feedback control. Input multiplicity arises when the same steady state output values can be reached with system inputs at different values. Dynamic systems with input multiplicities equipped with controllers with integral action have multiple stationary points, which may be locally stable or not. This is undesirable for operation. For a 2x2 example system with three stationary points we demonstrate how to design a set of two single loop controllers such that only one of the stationary points is locally stable, thus effectively eliminating the "input multiplicity problem" for control. We also show that when MPC is used for the example system, all three closed-loop stationary points are stable. Depending on the initial value of the input variables, the closed loop system under MPC may converge to different steady state input instances (but the same output steady state). Therefore we computationally explore the basin boundaries of this closed loop system. It is not clear how MPC or other modern nonlinear controllers could be designed so that only specific equilibrium points are stable.

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arXiv2022

Learning to Control Linear Systems can be Hard

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, i.e. exponentially, with the system dimension. This situation arises in the case of underactuated systems, i.e. 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.

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arXiv2022

Adaptive Stochastic MPC under Unknown Noise Distribution

In this paper, we address the stochastic MPC (SMPC) problem for linear systems, subject to chance state constraints and hard input constraints, under unknown noise distribution. First, we reformulate the chance state constraints as deterministic constraints depending only on explicit noise statistics. Based on these reformulated constraints, we design a distributionally robust and robustly stable benchmark SMPC algorithm for the ideal setting of known noise statistics. Then, we employ this benchmark controller to derive a novel robustly stable adaptive SMPC scheme that learns the necessary noise statistics online, while guaranteeing time-uniform satisfaction of the unknown reformulated state constraints with high probability. The latter is achieved through the use of confidence intervals which rely on the empirical noise statistics and are valid uniformly over time. Moreover, control performance is improved over time as more noise samples are gathered and better estimates of the noise statistics are obtained, given the online adaptation of the estimated reformulated constraints. Additionally, in tracking problems with multiple successive targets our approach leads to an online-enlarged domain of attraction compared to robust tube-based MPC. A numerical simulation of a DC-DC converter is used to demonstrate the effectiveness of the developed methodology.

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arXiv2022

Temporal Robustness of Temporal Logic Specifications: Analysis and Control Design

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 design problem in which we aim to design a control law that maximizes the temporal robustness of a dynamical system. Our solution consists of a Mixed-Integer Linear Programming (MILP) encoding that can be used to obtain a sequence of optimal control inputs. While asynchronous temporal robustness is arguably more nuanced than synchronous temporal robustness, we show that control design using synchronous temporal robustness is computationally more efficient. This trade-off can be exploited by the designer depending on the particular application at hand. We conclude the paper with a variety of case studies.

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arXiv2022

Robust Model Predictive Control with Polytopic Model Uncertainty through System Level Synthesis

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 numerical comparison of our method and representative robust MPC methods from the literature. Numerical examples demonstrate that our proposed method can significantly reduce the conservatism over a wide range of uncertainty parameters with comparable computational effort as the baseline methods.

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arXiv2021

System Level Synthesis-based Robust Model Predictive Control through Convex Inner Approximation

We propose a robust model predictive control (MPC) method for discrete-time linear time-invariant systems with norm-bounded additive disturbances and model uncertainty. In our method, at each time step we solve a finite time robust optimal control problem (OCP) which jointly searches over robust linear state feedback controllers and bounds the deviation of the system states from the nominal predicted trajectory. By leveraging the System Level Synthesis (SLS) framework, the proposed robust OCP is formulated as a convex quadratic program in the space of closed-loop system responses. When an adaptive horizon strategy is used, we prove the recursive feasibility of the proposed MPC controller and input-to-state stability of the origin for the closed-loop system. We demonstrate through numerical examples that the proposed method considerably reduces conservatism when compared with existing SLS-based and tube-based robust MPC methods, while also enjoying low computational complexity.

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arXiv2021

Learning Region of Attraction for Nonlinear Systems

Estimating the region of attraction (ROA) of general nonlinear autonomous systems remains a challenging problem and requires a case-by-case analysis. Leveraging the universal approximation property of neural networks, in this paper, we propose a counterexample-guided method to estimate the ROA of general nonlinear dynamical systems provided that they can be approximated by piecewise linear neural networks and that the approximation error can be bounded. Specifically, our method searches for robust Lyapunov functions using counterexamples, i.e., the states at which the Lyapunov conditions fail. We generate the counterexamples using Mixed-Integer Quadratic Programming. Our method is guaranteed to find a robust Lyapunov function in the parameterized function class, if exists, after collecting a finite number of counterexamples. We illustrate our method through numerical examples.

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arXiv2021

Learning $Q$-function approximations for hybrid control problems

The main challenge in controlling hybrid systems arises from having to consider an exponential number of sequences of future modes to make good long-term decisions. Model predictive control (MPC) computes a control action through a finite-horizon optimisation problem. A key ingredient in this problem is a terminal cost, to account for the system's evolution beyond the chosen horizon. A good terminal cost can reduce the horizon length required for good control action and is often tuned empirically by observing performance. We build on the idea of using $N$-step $Q$-functions $(\mathcal{Q}^{(N)})$ in the MPC objective to avoid having to choose a terminal cost. We present a formulation incorporating the system dynamics and constraints to approximate the optimal $\mathcal{Q}^{(N)}$-function and algorithms to train the approximation parameters through an exploration of the state space. We test the control policy derived from the trained approximations on two benchmark problems through simulations and observe that our algorithms are able to learn good $\mathcal{Q}^{(N)}$-approximations for high dimensional hybrid systems based on a relatively small dataset. Finally, we compare our controller's performance against that of Hybrid MPC in terms of computation time and closed-loop cost.

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arXiv2021

Time-Robust Control for STL Specifications

We present a robust control framework for time-critical systems in which satisfying real-time constraints robustly is of utmost importance for the safety of the system. Signal Temporal Logic (STL) provides a formal means to express a large variety of real-time constraints over signals and is suited for planning and control purposes as it allows us to reason about the time robustness of such constraints. The time robustness of STL particularly quantifies the extent to which timing uncertainties can be tolerated without violating real-time specifications. In this paper, we first pose a control problem in which we aim to find an optimal input sequence to a control system that maximizes the time robustness of an STL constraint. We then propose a Mixed Integer Linear Program (MILP) encoding and provide correctness guarantees along with a complexity analysis of the encoding. We also show in two case studies that maximizing STL time robustness allows to account for timing uncertainties of the underlying control system.

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arXiv2020

Learning Lyapunov Functions for Hybrid Systems

We propose a sampling-based approach to learn Lyapunov functions for a class of discrete-time autonomous hybrid systems that admit a mixed-integer representation. Such systems include autonomous piecewise affine systems, closed-loop dynamics of linear systems with model predictive controllers, piecewise affine/linear complementarity/mixed-logical dynamical system in feedback with a ReLU neural network controller, etc. The proposed method comprises an alternation between a learner and a verifier to find a valid Lyapunov function inside a convex set of Lyapunov function candidates. In each iteration, the learner uses a collection of state samples to select a Lyapunov function candidate through a convex program in the parameter space. The verifier then solves a mixed-integer quadratic program in the state space to either validate the proposed Lyapunov function candidate or reject it with a counterexample, i.e., a state where the Lyapunov condition fails. This counterexample is then added to the sample set of the learner to refine the set of Lyapunov function candidates. By designing the learner and the verifier according to the analytic center cutting-plane method from convex optimization, we show that when the set of Lyapunov functions is full-dimensional in the parameter space, our method finds a Lyapunov function in a finite number of steps. We demonstrate our stability analysis method on closed-loop MPC dynamical systems and a ReLU neural network controlled PWA system.

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arXiv2020

Stability Analysis of Complementarity Systems with Neural Network Controllers

Complementarity problems, a class of mathematical optimization problems with orthogonality constraints, are widely used in many robotics tasks, such as locomotion and manipulation, due to their ability to model non-smooth phenomena (e.g., contact dynamics). In this paper, we propose a method to analyze the stability of complementarity systems with neural network controllers. First, we introduce a method to represent neural networks with rectified linear unit (ReLU) activations as the solution to a linear complementarity problem. Then, we show that systems with ReLU network controllers have an equivalent linear complementarity system (LCS) description. Using the LCS representation, we turn the stability verification problem into a linear matrix inequality (LMI) feasibility problem. We demonstrate the approach on several examples, including multi-contact problems and friction models with non-unique solutions.

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arXiv2020

Learning Lyapunov Functions for Piecewise Affine Systems with Neural Network Controllers

We propose a learning-based method for Lyapunov stability analysis of piecewise affine dynamical systems in feedback with piecewise affine neural network controllers. The proposed method consists of an iterative interaction between a learner and a verifier, where in each iteration, the learner uses a collection of samples of the closed-loop system to propose a Lyapunov function candidate as the solution to a convex program. The learner then queries the verifier, which solves a mixed-integer program to either validate the proposed Lyapunov function candidate or reject it with a counterexample, i.e., a state where the stability condition fails. This counterexample is then added to the sample set of the learner to refine the set of Lyapunov function candidates. We design the learner and the verifier based on the analytic center cutting-plane method, in which the verifier acts as the cutting-plane oracle to refine the set of Lyapunov function candidates. We show that when the set of Lyapunov functions is full-dimensional in the parameter space, the overall procedure finds a Lyapunov function in a finite number of iterations. We demonstrate the utility of the proposed method in searching for quadratic and piecewise quadratic Lyapunov functions.

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arXiv2020

Learning to Track Dynamic Targets in Partially Known Environments

We solve active target tracking, one of the essential tasks in autonomous systems, using a deep reinforcement learning (RL) approach. In this problem, an autonomous agent is tasked with acquiring information about targets of interests using its onboard sensors. The classical challenges in this problem are system model dependence and the difficulty of computing information-theoretic cost functions for a long planning horizon. RL provides solutions for these challenges as the length of its effective planning horizon does not affect the computational complexity, and it drops the strong dependency of an algorithm on system models. In particular, we introduce Active Tracking Target Network (ATTN), a unified RL policy that is capable of solving major sub-tasks of active target tracking -- in-sight tracking, navigation, and exploration. The policy shows robust behavior for tracking agile and anomalous targets with a partially known target model. Additionally, the same policy is able to navigate in obstacle environments to reach distant targets as well as explore the environment when targets are positioned in unexpected locations.

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