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We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…
Linear Temporal Logic (LTL) is widely used to specify high-level objectives for system policies, and it is highly desirable for autonomous systems to learn the optimal policy with respect to such specifications. However, learning the…
This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation…
A novel approach to exploiting the log-convex structure present in many design problems is developed by modifying the classical Sequential Quadratic Programming (SQP) algorithm. The modified algorithm, Logspace Sequential Quadratic…
In this paper we study the relationship between the optimal value of a homogeneous quadratic optimization problem and that of its Semidefinite Programming (SDP) relaxation. We consider two quadratic optimization models: (1) $\min \{x^* C x…
In this paper, a novel Q-learning scheduling method for the current controller of switched reluctance motor (SRM) drive is investigated. Q-learning algorithm is a class of reinforcement learning approaches that can find the best…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…
This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…
We consider semidefinite programming (SDP) for the binary stochastic block model with equal-sized communities. Prior work of Hajek, Wu, and Xu proposed an SDP (sym-SDP) for the symmetric case where the intra-community edge probabilities are…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality…
Unlike traditional model-based reinforcement learning approaches that estimate system parameters from data, non-model-based data-driven control learns the optimal policy directly from input-state data without any intermediate model…
This paper is concerned with the linear quadratic optimal control of discrete-time time-varying system with terminal state constraint. The main contribution is to propose a Q-learning algorithm for the optimal controller when the…
Reinforcement learning (RL) is used to directly design a control policy using data collected from the system. This paper considers the robustness of controllers trained via model-free RL. The discussion focuses on the standard model-based…
In this paper, we study a class of nonsmooth fractional programs {\rm (FP, for short)} with SOS-convex semi-algebraic functions. Under suitable assumptions, we derive a strong duality result between the problem (FP) and its semidefinite…
Learning-based approaches, notably Reinforcement Learning (RL), have shown promise for solving optimal control tasks without explicit system models. However, these approaches are often sample-inefficient, sensitive to reward design and…
Motivated by applications in wireless communications, this paper develops semidefinite programming (SDP) relaxation techniques for some mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation…
In many practical control applications, the performance level of a closed-loop system degrades over time due to the change of plant characteristics. Thus, there is a strong need for redesigning a controller without going through the system…
We investigate the discrete-time stochastic linear quadratic control problem for a population of cooperative agents under the hard equality constraint on total control inputs, motivated by demand response in renewable energy systems. We…