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Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
This paper proposes a computationally tractable algorithm for learning infinite-horizon average-reward linear Markov decision processes (MDPs) and linear mixture MDPs under the Bellman optimality condition. While guaranteeing computational…
Classically, the optimal control problem in the presence of an adversary is formulated as a two-player zero-sum differential game or an $H_\infty$ control problem. The solution to these problems can be obtained by solving the…
Empowerment is an information-theoretic method that can be used to intrinsically motivate learning agents. It attempts to maximize an agent's control over the environment by encouraging visiting states with a large number of reachable next…
This work proposed an efficient learning-based framework to learn feedback control policies from human teleoperated demonstrations, which achieved obstacle negotiation, staircase traversal, slipping control and parcel delivery for a tracked…
We propose a new LMI approach to the design of optimal switching sequences for polynomial dynamical systems with state constraints. We formulate the switching design problem as an optimal control problem which is then relaxed to a linear…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
We propose a function-learning methodology with a control-theoretical foundation. We parametrise the approximating function as the solution to a control system on a reproducing-kernel Hilbert space, and propose several methods to find the…
This work presents a technique for learning systems, where the learning process is guided by knowledge of the physics of the system. In particular, we solve the problem of the two-point boundary optimal control problem of linear…
The quadratic optimal state feedback (LQR) is one of the most popular designs for linear systems and succeeds via the solution of the algebraic Riccati equation. The situation is different in the case of non-linear systems: the Riccati…
In this paper, a multi-objective model-following control problem is solved using an observer-based adaptive learning scheme. The overall goal is to regulate the model-following error dynamics along with optimizing the dynamic variables of a…
Closed-loop optimal control design for high-dimensional nonlinear systems has been a long-standing challenge. Traditional methods, such as solving the associated Hamilton-Jacobi-Bellman equation, suffer from the curse of dimensionality.…
Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case.…
The maximum hands-off control is the optimal solution to the L0 optimal control problem. It has the minimum support length among all feasible control inputs. To avoid computational difficulties arising from its combinatorial nature, the…
Optimal control provides a principled framework for transforming dynamical system models into intelligent decision-making, yet classical computational approaches are often too expensive for real-time deployment in dynamic or uncertain…
We consider a class of $\ell_0$-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator…
In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the…
We introduce the "inverse bandit" problem of estimating the rewards of a multi-armed bandit instance from observing the learning process of a low-regret demonstrator. Existing approaches to the related problem of inverse reinforcement…