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This article presents a unified approach to quadratic optimal control for both linear and nonlinear discrete-time systems, with a focus on trajectory tracking. The control strategy is based on minimizing a quadratic cost function that…
This article presents a method to automatically generate energy-optimal trajectories for systems with linear dynamics, linear constraints, and a quadratic cost functional (LQ systems). First, using recent advancements in optimal control, we…
The convergence of policy gradient algorithms in reinforcement learning hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of…
We study in this paper a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk…
We describe an optimal adversarial attack formulation against autoregressive time series forecast using Linear Quadratic Regulator (LQR). In this threat model, the environment evolves according to a dynamical system; an autoregressive model…
We introduce a generic solver for dynamic portfolio allocation problems when the market exhibits return predictability, price impact and partial observability. We assume that the price modeling can be encoded into a linear state-space and…
We propose a new risk-constrained reformulation of the standard Linear Quadratic Regulator (LQR) problem. Our framework is motivated by the fact that the classical (risk-neutral) LQR controller, although optimal in expectation, might be…
The convergence of policy gradient algorithms hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of linear quadratic control.…
Optimal control is often used in robotics for planning a trajectory to achieve some desired behavior, as expressed by the cost function. Most works in optimal control focus on finding a single optimal trajectory, which is then typically…
Many applications -- including power systems, robotics, and economics -- involve a dynamical system interacting with a stochastic and hard-to-model environment. We adopt a reinforcement learning approach to control such systems.…
We study in this paper the linear quadratic optimal control (linear quadratic regulation, LQR for short) for discrete-time complex-valued linear systems, which have shown to have several potential applications in control theory. Firstly, an…
It is well known that highly volatile control laws, while theoretically optimal for certain systems, are undesirable from an engineering perspective, being generally deleterious to the controlled system. In this article we are concerned…
Iterative linear quadratic regulator (iLQR) has gained wide popularity in addressing trajectory optimization problems with nonlinear system models. However, as a model-based shooting method, it relies heavily on an accurate system model to…
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…
For various typical cases and situations where the formulation results in an optimal control problem, the Linear Quadratic Regulator (LQR) approach and its variants continue to be highly attractive. In certain scenarios, it can happen that…
In this work, we consider the optimal portfolio selection problem under hard constraints on trading volume amounts when the dynamics of the risky asset returns are governed by a discrete-time approximation of the Markov-modulated geometric…
Periodic operation often emerges as the economically optimal mode in industrial processes, particularly under varying economic or environmental conditions. This paper proposes a robust model predictive control (MPC) framework for uncertain…
Recent strides in nonlinear model predictive control (NMPC) underscore a dependence on numerical advancements to efficiently and accurately solve large-scale problems. Given the substantial number of variables characterizing typical…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
Designing controllers to generate various trajectories has been studied for years, while recently, recovering an optimal controller from trajectories receives increasing attention. In this paper, we reveal that the inherent linear quadratic…