Charlott Vallon

Spencer Schutz, Charlott Vallon, Francesco Borrelli

In adaptive-sampling control, the control frequency can be adjusted during task execution. Ensuring that these on-the-fly changes do not jeopardize the safety of the system being controlled requires careful attention. We introduce robust M-step hold model predictive control (MPC) to address this. This MPC formulation provides robust constraint satisfaction for an uncertain discrete-time system model with a fixed sampling time subject to an adaptable multi-step input hold (referred to as M-step hold). We show how to ensure recursive feasibility of the MPC utilizing M-step hold extensions of robust invariant sets, and demonstrate how to use our framework to enable safe adaptive-sampling control via the online selection of M. We evaluate the utility of the robust M-step hold MPC formulation in a cruise control example.

Charlott Vallon, Francesco Borrelli

This article proposes a hierarchical learning architecture for safe data-driven control in unknown environments. We consider a constrained nonlinear dynamical system and assume the availability of state-input trajectories solving control tasks in different environments. In addition to task-invariant system state and input constraints, a parameterized environment model generates task-specific state constraints, which are satisfied by the stored trajectories. Our goal is to use these trajectories to find a safe and high-performing policy for a new task in a new, unknown environment. We propose using the stored data to learn generalizable control strategies. At each time step, based on a local forecast of the new task environment, the learned strategy consists of a target region in the state space and input constraints to guide the system evolution to the target region. These target regions are used as terminal sets by a low-level model predictive controller. We show how to i) design the target sets from past data and then ii) incorporate them into a model predictive control scheme with shifting horizon that ensures safety of the closed-loop system when performing the new task. We prove the feasibility of the resulting control policy, and apply the proposed method to robotic path planning, racing, and computer game applications.

Monimoy Bujarbaruah, Charlott Vallon, Francesco Borrelli

We propose a control design method for linear time-invariant systems that iteratively learns to satisfy unknown polyhedral state constraints. At each iteration of a repetitive task, the method constructs an estimate of the unknown environment constraints using collected closed-loop trajectory data. This estimated constraint set is improved iteratively upon collection of additional data. An MPC controller is then designed to robustly satisfy the estimated constraint set. This paper presents the details of the proposed approach, and provides robust and probabilistic guarantees of constraint satisfaction as a function of the number of executed task iterations. We demonstrate the safety of the proposed framework and explore the safety vs. performance trade-off in a detailed numerical example.

Monimoy Bujarbaruah, Charlott Vallon

This paper proposes an Adaptive Stochastic Model Predictive Control (MPC) strategy for stable linear time-invariant systems in the presence of bounded disturbances. We consider multi-input, multi-output systems that can be expressed by a Finite Impulse Response (FIR) model. The parameters of the FIR model corresponding to each output are unknown but assumed sparse. We estimate these parameters using the Recursive Least Squares algorithm. The estimates are then improved using set-based bounds obtained by solving the Basis Pursuit Denoising [1] problem. Our approach is able to handle hard input constraints and probabilistic output constraints. Using tools from distributionally robust optimization, we reformulate the probabilistic output constraints as tractable convex second-order cone constraints, which enables us to pose our MPC design task as a convex optimization problem. The efficacy of the developed algorithm is highlighted with a thorough numerical example, where we demonstrate performance gain over the counterpart algorithm of [2], which does not utilize the sparsity information of the system impulse response parameters during control design.

Charlott Vallon, Francesco Borrelli

A task decomposition method for iterative learning model predictive control is presented. We consider a constrained nonlinear dynamical system and assume the availability of state-input pair datasets which solve a task T1. Our objective is to find a feasible model predictive control policy for a second task, T2, using stored data from T1. Our approach applies to tasks T2 which are composed of subtasks contained in T1. In this paper we propose a formal definition of subtasks and the task decomposition problem, and provide proofs of feasibility and iteration cost improvement over simple initializations. We demonstrate the effectiveness of the proposed method on autonomous racing and robotic manipulation experiments.