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Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…
We consider the problem of reinforcement learning using function approximation, where the approximating basis can change dynamically while interacting with the environment. A motivation for such an approach is maximizing the value function…
This paper provides an approximate online adaptive solution to the infinite-horizon optimal tracking problem for control-affine continuous-time nonlinear systems with unknown drift dynamics. Model-based reinforcement learning is used to…
Discrete time stochastic optimal control problems and Markov decision processes (MDPs), respectively, serve as fundamental models for problems that involve sequential decision making under uncertainty and as such constitute the theoretical…
This paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm-bounded parametric uncertainties and disturbances, and in presence of some amplitude constraints on the control…
We study the adaptive control of an unknown linear system with a quadratic cost function subject to safety constraints on both the states and actions. The challenges of this problem arise from the tension among safety, exploration,…
The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems…
This paper considers the problem of adapting a predesigned policy, represented by a parameterized function class, from a solution that minimizes a given original cost function to a trade-off solution between minimizing the original…
For an infinite-horizon control problem, the optimal control can be represented by the stable manifold of the characteristic Hamiltonian system of Hamilton-Jacobi-Bellman (HJB) equation in a semiglobal domain. In this paper, we first…
In this paper, we present a novel method for computing the optimal feedback gain of the infinite-horizon Linear Quadratic Regulator (LQR) problem via an ordinary differential equation. We introduce a novel continuous-time Bellman error,…
In this paper we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. The proposed approach leverages physics-informed machine learning to solve high-dimensional Hamilton-Jacobi-Bellman…
We consider the problem of discounted optimal state-feedback regulation for general unknown deterministic discrete-time systems. It is well known that open-loop instability of systems, non-quadratic cost functions and complex nonlinear…
We present a novel class of minimax optimal control problems with positive dynamics, linear objective function and homogeneous constraints. The proposed problem class can be analyzed with dynamic programming and an explicit solution to the…
This work is concerned with solving neural network-based feedback controllers efficiently for optimal control problems. We first conduct a comparative study of two prevalent approaches: offline supervised learning and online direct policy…
We consider the problem of learning a linear control policy for a linear dynamical system, from demonstrations of an expert regulating the system. The standard approach to this problem is policy fitting, which fits a linear policy by…
This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for…
This paper presents a study of the Koopman operator theory and its application to optimal control of a multi-robot system. The Koopman operator, while operating on a set of observation functions of the state vector of a nonlinear system,…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
This paper introduces an optimal control framework to address the inverse problem using a learned regularizer, with applications in image reconstruction. We build upon the concept of Learnable Optimization Algorithms (LOA), which combine…
We propose and analyze a reinforcement learning principle that approximates the Bellman equations by enforcing their validity only along an user-defined space of test functions. Focusing on applications to model-free offline RL with…