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In this paper, Second Derivative Method (SDM) of numerical discretization is applied to optimal control problems. Convergence rates for the error between the discretized solution of SDM and the corresponding analytical solution of optimal control problems are analyzed. Illustrative examples are included to demonstrate the applicability and benefits of SDM. The comparison of the convergence rates of...
We develop a customized method of multipliers algorithm to efficiently solve a class of regularized optimal control problems. By exploiting the problem structure, we transform the augmented Lagrangian into a form which can be efficiently minimized using proximal methods. We apply our algorithm to an ℓ1-regularized state-feedback optimal control problem and compare its performance with a proximal gradient...
Nonlinear Model Predictive Control (NMPC) relies on solving an Optimal Control Problem (OCP) online at every sampling time. The discretization of the continuous time dynamics requires the deployment of some numerical integration method. To that end, implicit integrators are often preferred when stiff or implicitly defined dynamics are present in the system. Implicit integration schemes, however, are...
The Algebraic Riccati Equation (ARE) has increasingly played its role for the optimal control theory [1], [2]. Adaptive filters have been a widely used technique in the context of real time solution for ARE [3]. The least mean square (LMS) and the recursive least square (RLS) are among the most well known filters [4], [5]. Nevertheless, these algorithms have a lower learning rate for multivariable...
This paper studies an optimization-based approach for solving optimal estimation and optimal control problems through a unified computational formulation. The goal is to perform trajectory estimation over extended past horizons and model-predictive control over future horizons by enforcing the same dynamics, control, and sensing constraints in both problems, and thus solving both problems with identical...
The paper is aimed at the definition of an efficient control framework for freeway systems. To this end, a Model Predictive Control scheme based on the cell transmission model is adopted in which the considered control action refers to ramp metering. Two major aspects characterize the paper. First, the prediction model is formulated as a mixed logical dynamical system (i.e. it is described by linear...
Singular controls are usually idealizations of controls that are large and occur over a small but non-zero amount of time, or else are limits of a sequence of small impulses occurring close together. When these control terms are multiplied by a function of the state, it is what we call “state-dependence.” Because of this state-dependence, there usually are problems in using standard weak convergence...
This paper focuses on the problem of optimizing the trajectories of multiple searchers attempting to detect a non-evading moving target whose motion is conditionally deterministic. This problem is a parameter-distributed optimal control problem, as it involves an integration over a space of stochastic parameters as well as an integration over the time domain. In this paper, we consider a wide range...
In case of linear quadratic regulator (LQR), the updated terminal cost receding horizon control (UTC-RHC) enhances the standard RHC in terms of the stability and the convergence to the optimal solution. Based on the action-dependent (AD) value functions, known as Q-function, this paper proposes two modified RHC methods, AD-RHC and AD-UTC-RHC and proves the stability and convergence by using the matrix...
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