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This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between…
This paper investigates the performance of Newton's method, iterative Linear Quadratic Regulator (iLQR), and Differential Dynamic Programming (DDP) in solving discrete-time optimal control problems. We offer a unified perspective on these…
This paper provides an overview, analysis, and comparison of second-order dynamic optimization algorithms, i.e., constrained Differential Dynamic Programming (DDP) and Sequential Quadratic Programming (SQP). Although a variety of these…
Indirect trajectory optimization methods such as Differential Dynamic Programming (DDP) have found considerable success when only planning under dynamic feasibility constraints. Meanwhile, nonlinear programming (NLP) has been the…
Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
In this paper, we consider the linear programming (LP) formulation for deep reinforcement learning. The number of the constraints depends on the size of state and action spaces, which makes the problem intractable in large or continuous…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
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,…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm…
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…
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…
We develop a Sequential Quadratic Optimization (SQP) algorithm for minimizing a stochastic objective function subject to deterministic equality constraints. The method utilizes two different stepsizes, one which exclusively scales the…
This paper presents a state and state-input constrained variant of the discrete-time iterative Linear Quadratic Regulator (iLQR) algorithm, with linear time-complexity in the number of time steps. The approach is based on a projection of…
This article explores the discrete-time stochastic optimal LQR control with delay and quadratic constraints. The inclusion of delay, compared to delay-free optimal LQR control with quadratic constraints, significantly increases 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…
We present a new algorithm for solving linear-quadratic regulator (LQR) problems with linear equality constraints, also known as constrained LQR (CLQR) problems. Our method's sequential runtime is linear in the number of stages and…
This paper considers smooth convex optimization problems with many functional constraints. To solve this general class of problems we propose a new stochastic perturbed augmented Lagrangian method, called SGDPA, where a perturbation is…