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We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
Linear-Quadratic optimal controls are computed for a class of boundary controlled, boundary observed hyperbolic infinite-dimensional systems, which may be viewed as networks of waves. The main results of this manuscript consist in…
This paper is concerned with the distributed linear quadratic optimal control problem. In particular, we consider a suboptimal version of the distributed optimal control problem for undirected multi-agent networks. Given a multi-agent…
This paper considers the stochastic linear quadratic optimal control problem in which the control domain is nonconvex. By the functional analysis and convex perturbation methods, we establish a novel maximum principle. The application of…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
Inexact methods for model predictive control (MPC), such as real-time iterative schemes or time-distributed optimization, alleviate the computational burden of exact MPC by providing suboptimal solutions. While the asymptotic stability of…
These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…
A fundamental challenge in multiagent systems is to design local control algorithms to ensure a desirable collective behaviour. The information available to the agents, gathered either through communication or sensing, naturally restricts…
We address the problem of multiple local optima commonly arising in optimization problems for multi-agent systems, where objective functions are nonlinear and nonconvex. For the class of coverage control problems, we propose a systematic…
This paper is concerned with a kind of linear-quadratic (LQ) optimal control problem of backward stochastic differential equation (BSDE) with partial information. The cost functional includes cross terms between the state and control, and…
In this paper, we demonstrate a formulation for optimizing coupled submodular maximization problems with provable sub-optimality bounds. In robotics applications, it is quite common that optimization problems are coupled with one another…
Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…
This paper proposes a method to compute lower performance bounds for discrete-time infinite-horizon min-max control problems with input constraints and bounded disturbances. Such bounds can be used as a performance metric for control…
We consider a class of multi-agent optimal coverage problems in which the goal is to determine the optimal placement of a group of agents in a given mission space so that they maximize a coverage objective that represents a blend of…
We introduce the concept of a sum-rank saturating system and outline its correspondence to a covering properties of a sum-rank metric code. We consider the problem of determining the shortest sum-rank-$\rho$-saturating systems of a fixed…
When deploying autonomous agents in unstructured environments over sustained periods of time, adaptability and robustness oftentimes outweigh optimality as a primary consideration. In other words, safety and survivability constraints play a…
We analyze the performance of policy gradient in multitask linear quadratic regulation (LQR), where the system and cost parameters differ across tasks. The main goal of multitask LQR is to find a controller with satisfactory performance on…
The present work deals with quantitative two-phase reach-avoid problems on nonlinear control systems. This class of optimal control problem requires the plant's state to visit two (rather than one) target sets in succession while minimizing…
Iterative learning control (ILC) is a powerful technique for high performance tracking in the presence of modeling errors for optimal control applications. There is extensive prior work showing its empirical effectiveness in applications…
We introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation. It is based on a sum-of-squares representation of the Hamiltonian, and extends a previous method from polynomial…