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Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
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…
The challenge of constructing feedback control laws for risk-averse optimal control of partial differential equations (PDEs) with random coefficients is addressed. The control objective composes a tracking-type cost with the nonlinear…
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
This paper addresses a risk-constrained decentralized stochastic linear-quadratic optimal control problem with one remote controller and one local controller, where the risk constraint is posed on the cumulative state weighted variance in…
Piecewise constant control approximation provides a practical framework for designing numerical schemes of continuous-time control problems. We analyze the accuracy of such approximations for extended mean field control (MFC) problems,…
In this paper, we consider two sequential decision making problems with a convexity structure, namely an energy storage optimization task and a multi-product assembly example. We formulate these problems in the stochastic programming…
Predictive control is frequently used for control problems involving constraints. Being an optimization based technique utilizing a user specified so-called stage cost, performance properties, i.e., bounds on the infinite horizon…
The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The algorithms and theory rest on a relaxation of a dual of Manne's celebrated linear programming characterization of…
A self-learning optimal control algorithm for episodic fixed-horizon manufacturing processes with time-discrete control actions is proposed and evaluated on a simulated deep drawing process. The control model is built during consecutive…
In this paper, we propose a new policy iteration algorithm to compute the value function and the optimal controls of continuous time stochastic control problems. The algorithm relies on successive approximations using linear-quadratic…
This note presents an extension to the adaptive control strategy presented in [1] able to counter eventual instability due to disturbances at the input of an otherwise $\mathcal{L}_2$ stable closed-loop system. These disturbances are due to…
The convex analytic method has proved to be a very versatile method for the study of infinite horizon average cost optimal stochastic control problems. In this paper, we revisit the convex analytic method and make three primary…
Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems. Based on dynamic programming, their key feature is the approximation of the conditional expectation of future rewards by…
Periodic dynamical systems, distinguished by their repetitive behavior over time, are prevalent across various engineering disciplines. In numerous applications, particularly within industrial contexts, the implementation of model…
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
This paper first presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Then, by introducing several sequences of bounded linear operators, the…