Related papers: Optimal Control for Linear Systems with L1-norm co…
This paper is dedicated to the stability analysis of the optimal solutions of a control problem associated with a semilinear elliptic equation. The linear differential operator of the equation is neither monotone nor coercive due to the…
We consider left-invariant optimal control problems on connected Lie groups such that generic stabilizer of the coadjoint action is connected and has dimension not more than 1. We introduce a construction for symmetries of the exponential…
In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost…
Stability and control of a non-linear system represent an important system configuration that frequently arises in practical engineering. Stability covers a vast range of systems that do not obey the superposition principle and applies to…
The paper deals with initial-boundary value problems for linear non-autonomous first order hyperbolic systems whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in $L^2$ as…
This paper revisits the classical Linear Quadratic Gaussian (LQG) control from a modern optimization perspective. We analyze two aspects of the optimization landscape of the LQG problem: 1) connectivity of the set of stabilizing controllers…
We consider scalar decentralized average-cost infinite-horizon LQG problems with two controllers, focusing on the fast dynamics case when the (scalar) eigenvalue of the system is large. It is shown that the best linear controllers'…
We consider a system that is exactly controllable. For given initial state, terminal state and objective function, an optimal control is often well-defined. Such an optimal control has the disadvantage that although it works perfectly well…
This paper investigates the robustness of stochastic optimal control for controlled regime switching diffusions. We consider systems driven by both continuous fluctuations and discrete regime changes, allowing for model misspecification in…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…
In the contest of optimal control problems, regularity results for optima are known when addressing fiber-strictly convex Lagrangian. For infinite time horizons, or for settings with infinite dimensional dynamics, the equivalence between…
This paper presents novel controllers that yield finite-time stability for linear systems. We first present a sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finite-time controllers…
Suboptimal methods in optimal control arise due to a limited computational budget, unknown system dynamics, or a short prediction window among other reasons. Although these methods are ubiquitous, their transient performance remains…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
Maximum hands-off control is a control that has the minimum L0 norm among all feasible controls. It is known that the maximum hands-off (or L0-optimal) control problem is equivalent to the L1-optimal control under the assumption of…
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. It is known that these problems are related to certain infinite-dimensional linear programming…
In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. We propose…
This paper investigates the finite time stabilization problem for a class of nonlinear systems with unknown control directions and unstructured uncertainties. The unstructured uncertainties indicate that not only the parameters but also the…
The Lyapunov inequality is an indispensable tool for stability analysis in linear control theory. It provides a necessary and sufficient condition for the stability of an autonomous linear-time invariant system in terms of the existence of…