Neural dynamic optimization for control systems. I. Background

The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper mainly describes the background and motivations for the development of NDO, while the two other subsequent papers of this topic present the theory of NDO and demonstrate the method with several applications including control of autonomous vehicles and of a robot arm, respectively.     

Neural dynamic optimization for control systems.II. Theory

The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper mainly describes the theory of NDO, while the two other companion papers of this topic explain the background for the development of NDO and demonstrate the method with several applications including control of autonomous vehicles and of a robot arm, respectively.     

Discrete optimization by optimal control methods. III. The dynamic traveling salesman problem

For one of the basic variants of the dynamic minisum traveling salesman problem, a decomposition scheme is designed, which in general gives a new approximate solution algorithm. This algorithm is exact if certain conditions are imposed on the distance matrix. The problem is solved with the sufficient optimality conditions known in optimal control theory.     

Neural network control of nonlinear dynamic systems using hybrid algorithm

In this paper, a hybrid method is proposed to control a nonlinear dynamic system using feedforward neural network. This learning procedure uses different learning algorithm separately. The weights connecting the input and hidden layers are firstly adjusted by a self organized learning procedure, whereas the weights between hidden and output layers are trained by supervised learning algorithm, such as a gradient descent method. A comparison with backpropagation (BP) shows that the new algorithm can considerably reduce network training time.     

基于动态观测器零极点优化的网络控制系统故障检测

针对网络化控制系统中在有限频扰动和噪声下的传感器故障检测问题,构建一种新型的观测器结构:动态观测器.利用动态观测器零点可配置这一新特性,提出零点和极点联合优化配置的故障检测方法.所提出的动态观测器是在传统比例积分观测器的基础上扩展而成,更具一般性,具有零点可配置的特点,能够克服传统观测器零点是固定的限制.将动态观测器的...     

A hybrid model-based optimal control method for nonlinear systems using simultaneous dynamic optimization strategies

To improve the overall control performance of nonlinear systems, an optimal control method, based on the framework of hybrid systems, is proposed. Firstly, the nonlinear systems are approximated by a number of piecewise affine models which are produced by the nonlinear systems at the specified operating points, then the piecewise affine models are synthesized under the framework of hybrid systems, and an associated optimal control problem, in which decision variables involve not only admissible continuous control but also the scheduling of subsystem modes, is established. Secondly, the optimal control problem is transformed into a MIQP problem by discretization over the whole state space and admissible control space to obtain the numerical optimal solution. For speeding up the algorithm, the simultaneous method on finite elements is used to lower the dimensions of the MIQP problem. Consequently, a hybrid model-based MPC for nonlinear systems is designed, and the adverse effects of model mismatch resulted from simultaneous method is weakened by MPC strategy. Simulations and comparisons with soft-switching method, hard-switching method and MLD method, confirm that a satisfactory performance can be obtained using the presented approach.     

Conic optimization for control,energy systems,and machine learning: Applications and algorithms

Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic programming. The recent advances in various topics of modern optimization have also been revamping the area of machine learning. Motivated by the crucial role of optimization theory in the design, analysis, control and operation of real-world systems, this tutorial paper offers a detailed overview of some major advances in this area, namely conic optimization and its emerging applications. First, we discuss the importance of conic optimization in different areas. Then, we explain seminal results on the design of hierarchies of convex relaxations for a wide range of nonconvex problems. Finally, we study different numerical algorithms for large-scale conic optimization problems.     

Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems

In this work, we propose a conceptual framework for integrating dynamic economic optimization and model predictive control (MPC) for optimal operation of nonlinear process systems. First, we introduce the proposed two-layer integrated framework. The upper layer, consisting of an economic MPC (EMPC) system that receives state feedback and time-dependent economic information, computes economically optimal time-varying operating trajectories for the process by optimizing a time-dependent economic cost function over a finite prediction horizon subject to a nonlinear dynamic process model. The lower feedback control layer may utilize conventional MPC schemes or even classical control to compute feedback control actions that force the process state to track the time-varying operating trajectories computed by the upper layer EMPC. Such a framework takes advantage of the EMPC ability to compute optimal process time-varying operating policies using a dynamic process model instead of a steady-state model, and the incorporation of suitable constraints on the EMPC allows calculating operating process state trajectories that can be tracked by the control layer. Second, we prove practical closed-loop stability including an explicit characterization of the closed-loop stability region. Finally, we demonstrate through extensive simulations using a chemical process model that the proposed framework can both (1) achieve stability and (2) lead to improved economic closed-loop performance compared to real-time optimization (RTO) systems using steady-state models.     

Neural approximations for infinite-horizon optimal control of nonlinear stochastic systems.

A feedback control law is proposed that drives the controlled vector v(t) of a discrete-time dynamic system to track a reference v(t)* over an infinite time horizon, while minimizing a given cost function. The behavior of v(t)* over time is completely unpredictable, Random noises act on the dynamic system and the state observation channel, which may be nonlinear. It is assumed that all such random vectors are mutually independent, and that their probability density functions are known. So general a non-LQG optimal control problem is very difficult to solve. The proposed solution is based on three main approximating assumptions: 1) the problem is stated in a receding-horizon framework where v(t)* is assumed to remain constant within a shifting-time window; 2) the control law is assigned a given structure (that of a multilayer feedforward neural net) in which a finite number of parameters have to be determined so as to minimize the cost function; and 3) the control law is given a limited memory, which prevents the amount of data to be stored from increasing over time. Errors resulting from the second and third assumptions are discussed, Due to the very general assumptions under which the control law is derived, we are not able to report stability results. However, simulation results show that the proposed method may constitute an effective tool for solving, to a sufficient degree of accuracy, a wide class of control problems traditionally regarded as difficult ones. An example of freeway traffic optimal control is given.     

Interactive design optimization of dynamic systems

This paper describes an interactive environment for dynamic response optimization problems. It is shown that with proper interactive facilities and designer intervention, the optimal design process can be more flexible, efficient and effective in solving practical design problems. The process can be initiated with a rough design model for the problem. As the iterations progress and insight is gained into the problem, the model can be interactively refined, without stopping the process, to obtain the final solution. Two example problems — a system dynamics problem and a control problem — are used to study and show advantages of the designer interaction. It is concluded that interactive optimum design capabilities offer more opportunities to the designer to obtain better designs.     

基于改进粒子群优化算法的离散混沌系统神经滑模控制

针对离散混沌系统,提出一种基于融合Powell法的粒子群优化策略(Powell-PSO算法)的神经滑模等效控制方法。该方法通过将BP神经网络的输出作为滑模等效控制的切换部分的系数,有效地克服了传统滑模等效控制的抖振现象;利用Powell-PSO算法对神经滑模控制器的参数进行全局优化,提高了离散混沌系统的控制品质。仿真实验结果表明,所提出的方法无需了解离散混沌系统精确模型,具有响应速度快、控制精度高以及抗干扰能力强的优点。     

Robust control techniques for general dynamic systems

Lyapunov techniques are used to design robust controllers for nonlinear systems. The objective is to use the system structure to simplify the controller as far as possible. A general robust control scheme is developed that applies to systems described by a class of second-order nonlinear equations. Applications to a mobile robot and a chemical stirred tank reactor are given.     

Real-time dynamic optimization of batch systems

In this paper a methodology for designing and implementing a real-time optimizing controller for batch processes is proposed. The controller is used to optimize a user-defined cost function subject to a parameterization of the input trajectories, a nominal model of the process and general state and input constraints. An interior point method with penalty function is used to incorporate constraints into a modified cost functional, and a Lyapunov based extremum seeking approach is used to compute the trajectory parameters. The technique is applicable to general nonlinear systems. A precise statement of the numerical implementation of the optimization routine is provided. It is shown how one can take into account the effect of sampling and discretization of the parameter update law in practical situations. A simulation example demonstrates the applicability of the technique.     

Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form

The dynamic surface control (DSC) technique was developed recently by Swaroop et al. This technique simplified the backstepping design for the control of nonlinear systems in strict-feedback form by overcoming the problem of "explosion of complexity." It was later extended to adaptive backstepping design for nonlinear systems with linearly parameterized uncertainty. In this paper, by incorporating this design technique into a neural network based adaptive control design framework, we have developed a backstepping based control design for a class of nonlinear systems in strict-feedback form with arbitrary uncertainty. Our development is able to eliminate the problem of "explosion of complexity" inherent in the existing method. In addition, a stability analysis is given which shows that our control law can guarantee the uniformly ultimate boundedness of the solution of the closed-loop system, and make the tracking error arbitrarily small.     

A hierarchical optimization neural network for large-scale dynamic systems

A recurrent neural network for dynamical hierarchical optimization of nonlinear discrete large-scale systems is presented. The proposed neural network consists of hierarchically structured sub-networks: one coordination sub-network at the upper level and several local optimization sub-networks at the lower level. In particular, the coordination sub-network and the local optimization sub-networks work simultaneously. This feature makes the proposed method outperform in computational efficiency the conventional iterative algorithms where there usually exists an alternately waiting time during the coordination and local optimization processes. Moreover, the state equations of the subsystems of the large-scale system are imbedded into their corresponding local optimization sub-networks. This imbedding technique not only overcomes the difficulty in treating the constraints imposed by the state equations, but also leads to significant reduction in the network size. We present stability analysis to prove that the neural network is asymptotically stable and this stable state corresponds to the optimal solution to the original optimal control problem. Finally, we illustrate the performance of the proposed method by an example.     

Neural networks for feedback feedforward nonlinear control systems

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.