We present a method of solving the T-optimal design problem for nonlinear dynamical systems using dynamic programming. In contrast with previous dynamic programming formulations, we avoid adding an equation for the dispersion to the system state, allowing for more efficient solutions.
This note describes a reference governor design for a continuous-time nonlinear system with an additive disturbance. The design is based on predicting the response of the nonlinear system by the response of a linear model with a set-bounded prediction error, where a state-and-input dependent bound on the prediction error is explicitly characterized using logarithmic norms. The online optimization is reduced to a convex quadratic program with linear inequality constraints. Two numerical examples are reported.
We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This problem is considerably more complicated than previous studies on covariance control for linear systems. We leverage a widely used technique - differential dynamic programming - in nonlinear optimal control to achieve our goal. In particular, we adopt the stochastic differential dynamic programming framework to handle the stochastic dynamics. Additionally, to enfo…
In this work, we present a learning-based nonlinear $H^\infty$ control algorithm that guarantee system performance under learned dynamics and disturbance estimate. The Gaussian Process (GP) regression is utilized to update the nominal dynamics of the system and provide disturbance estimate based on data gathered through interaction with the system. A soft-constrained differential game associated with the disturbance attenuation problem in nonlinear $H^\infty$ control is then formulated to obtain the nonlinear $H^\infty$ controller. The differential game is solved through the min-max Game-Theor…
Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates
Google Brain, Seattle, USA（谷歌大脑）；Paul G. Allen School of Computer Science and Engineering, University of Washington, Seattle, USA（保罗·G·艾伦计算机科学与工程学院）；Department of Electrical and Computer Engineering, University of Washington, Seattle, USA（电气与计算机工程系）；Department of Statistics University of Washington, Seattle, USA（统计学系）
Models can be built directly from input and output data trough a process known as system identification. The Nonlinear AutoRegressive with eXogenous inputs (NARMAX) models are among the most used mathematical representations in the area and has many successful applications on data-driven modeling in different fields. Such models become extremely large when they have high degree of non-linearity and long-term dependencies. Hence, a structure selection process must be performed to make them parsimonious. In the present paper, it is introduced a toolbox in Python that performs the structure selec…
This paper proposes the deployment of the Hopfield's artificial neural network (H-NN) approach to optimally assign power in optical code division multiple access (OCDMA) systems. Figures of merit such as feasibility of solutions and complexity are compared with the classical power allocation methods found in the literature, such as Sequential Quadratic Programming (SQP) and Augmented Lagrangian Method (ALM). The analyzed methods are used to solve constrained nonlinear optimization problems in the context of resource allocation for optical networks, specially to deal with the energy efficiency …
This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state constraints. Firstly, a constrained generalized policy iteration (CGPI) framework is developed to handle state constraints by transforming the traditional policy improvement process into a constrained policy optimization problem. Next, we propose an actor-critic variant of CGPI, called CADP, in which both policy and value functions are approximated by multi…
In this paper, we propose an approach to coordinated receding-horizon control of vehicle speed and transmission gearshift for automated battery electric vehicles (BEVs) to achieve improved energy efficiency. The introduction of multi-speed transmissions in BEVs creates an opportunity to manipulate the operating point of electric motors under given vehicle speed and acceleration command, thus providing the potential to further improve the energy efficiency. However, co-optimization of vehicle speed and transmission gearshift leads to a mixed integer nonlinear program (MINLP), solving which can …
We present an algorithm, based on the Differential Dynamic Programming framework, to handle trajectory optimization problems in which the horizon is determined online rather than fixed a priori. This algorithm exhibits exact one-step convergence for linear, quadratic, time-invariant problems and is fast enough for real-time nonlinear model-predictive control. We show derivations for the nonlinear algorithm in the discrete-time case, and apply this algorithm to a variety of nonlinear problems. Finally, we show the efficacy of the optimal-horizon model-predictive control scheme compared to a sta…
Real-Time Nonlinear MPC via Sequential Quadratic Programming with Structure-Exploiting ADMM and Interior-Point Methods for Underactuated Double-Pendulum Swing-Up
This is part I of the follow-up lecture notes of the lectures given by the authors at the Three \CO" (Composability, Comprehensibility, Correctness) Winter School held in Košice, Slovakia, in January 2018, and Summer School held in Budapest, Hungary, in June 2019. In this part we explain the role of functional programming paradigm in the management of complex software systems, and how the functional programming concepts play important role in the designing such systems. Key prerequisite for implementing functional programming concepts is properly designed system structure following well define…
