Dynamic programming for optimal packet routing control using two neural networks

We investigate packet flow in computer networks within the framework of statistical physics by using numerical simulations. As mathematical models for packet routing, we present a spin model with lattice gas spins and the one with Ising spins. Then we propose dynamic programming for optimal routing control of packet flow by using the two spin models. This is a kind of goal-directed learning for taking into account of time-dependent environment for the packets. Next we investigate a congestion problem by using the model with lattice gas spins when the packets are not sent to nodes at which their buffers are already full up with packets. Since we have found serious congestion in the packet flow, we then propose reinforcement learning for avoiding the congestion and have performed simulations on several networks including small world networks, scale free networks and so on.

In this paper, an infinite horizon optimal robust guaranteed cost control scheme of a class of continuous-time uncertain nonlinear systems is established based on adaptive dynamic programming. The main idea lies in that the optimal robust guaranteed cost control problem can be transformed into an optimal control problem. Actually, the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to help solving the modified Hamilton-Jacobi-Bellman equation corresponding to the nominal system. Then, an additional stabilizing term is introduced to reinforce the updating process of the weight vector and reduce the requirement of an initial stabilizing control. An example is provided to illustrate the effectiveness of the present control approach.

Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of SCP has received comparatively limited attention, and it is often restricted to discrete-time formulations. In this paper, we present a unifying theoretical analysis of a fairly general class of SCP procedures for continuous-time optimal control problems. In addition to the derivation of convergence guarantees in a continuous-time setting, our analysis reveals two new numerical and practical insights. First, we show how one can more easily account for manifold-type constraints, which are a defining feature of optimal control of mechanical systems. Second, we show how our theoretical analysis can be leveraged to accelerate SCP-based optimal control methods by infusing techniques from indirect optimal control.

Combining an Optimal Control Program with the Time Series Processor System

1 A Survey on Computational Optimal Control.- Issues in the Direct Transcription of Optimal Control Problems to Sparse Nonlinear Programs.- Optimization in Control of Robots.- Large-scale SQP Methods and their Application in Trajectory Optimization.- Solving Optimal Control and Pursuit-Evasion Game Problems of High Complexity.- 2 Theoretical Aspects of Optimal Control and Nonlinear Programming.- Continuation Methods In Boundary Value Problems.- Second Order Optimality Conditions for Singular Extremals.- Synthesis of Adaptive Optimal Controls for Linear Dynamic Systems.- Control Applications of Reduced SQP Methods.- Time Optimal Control of Mechanical Systems.- 3 Algorithms for Optimal Control Calculations.- Second Order Algorithm for Time Optimal Control of a Linear System.- An SQP-type Solution Method for Constrained Discrete-Time Optimal Control Problems.- Numerical Methods for Solving Differential Games, Prospective Applications to Technical Problems.- Construction of the Optimal Feedback Controller for Constrained Optimal Control Problems with Unknown Disturbances.- Repetitive Optimization for Predictive Control of Dynamic Systems under Uncertainty.- Optimal Control of Multistage Systems Described by High-Index Differential-Algebraic Equations.- A New Class of a High Order Interior Point Method for the Solution of Convex Semiinfinite Optimization Problems.- A Structured Interior Point SQP Method for Nonlinear Optimal Control Problems.- 4 Software for Optimal Control Calculations.- Automated Approach for Optimizing Dynamic Systems.- ANDECS: A Computation Environment for Control Applications of Optimization.- Application of Automatic Differentiation to Optimal Control Problems.- OCCAL: A mixed symbolic-numeric Optimal Control CALculator.- 5 Applications of Optimal Control.- A Robotic Satellite with Simplified Design.- Nonlinear Control under Constraints of a Biological System.- An Object-Oriented Approach to Optimally Describe and Specify a SCADA System Applied to a Power Network.- Near-Optimal Flight Trajectories Generated by Neural Networks.- Performance of a Feedback Method with Respect to Changes in the Air-Density during the Ascent of a Two-Stage-To-Orbit Vehicle.- Linear Optimal Control for Reentry Flight.- Steady-State Modelling of Turbine Engine with Controllers.- Shortest Paths for Satellite Mounted Robot Manipulators.- Optimal Control of the Industrial Robot Manutec r3.

A distributed parameter thermal and stress model is developed for a nuclear rocket. The resultant equations for the optimal control problem are a pair of coupled, bilinear, partial differential equations. The thermal stress constraint forms an inequality which is a function of both the state and the control. The initial conditions are steady state, and the terminal condition is that the coolant flow obtain a fixed, higher level. The distributed parameter system is discretized in the space dimension to give an arbitrary order set of ordinary differential, state equations. It is shown how a result based on the Weierstrass necessary condition and derived by Berkovitz from the calculus of variations using a slack variable technique may be applied. This condition is shown to require the optimal control to be “boundary control” with no switching. The optimal control program must make the inequality constraint an equality at some location throughout the transient. Based on the result that boundary control is the optimal control, an algorithm is developed to compute the optimal control program. The algorithm was programmed on a digital computer and numerical results are given for the optimal flow program and the resultant stress distributions for various cases.

For discrete-time nonlinear systems, this research is concerned with optimal control problems (OCPs) with constrained cost, and a novel value iteration with constrained cost (VICC) method is developed to solve the optimal control law with the constrained cost functions. The VICC method is initialized through a value function constructed by a feasible control law. It is proven that the iterative value function is nonincreasing and converges to the solution of the Bellman equation with constrained cost. The feasibility of the iterative control law is proven. The method to find the initial feasible control law is given. Implementation using neural networks (NNs) is introduced, and the convergence is proven by considering the approximation error. Finally, the property of the present VICC method is shown by two simulation examples.

Neuro-dynamic programming for optimal control of macroscopic fundamental diagram systems

Demonstrated is an optimal control solution to change of machine setup scheduling based on dynamic programming average cost per stage value iteration as set forth by M. Caramanis et al. (1991) for the 2-D case. The difficulty with the optimal approach lies in the explosive computational growth of the resulting solution. A method of reducing the computational complexity is developed using ideas from biology and neural networks. A real-time controller is described that uses a linear-log representation of state space with neural networks employed to fit cost surfaces. >

This paper studies data-driven learning-based methods for the finite-horizon optimal control of linear time-varying discrete-time systems. First, a novel finite-horizon Policy Iteration (PI) method for linear time-varying discrete-time systems is presented. Its connections with existing infinite-horizon PI methods are discussed. Then, both data-driven off-policy PI and Value Iteration (VI) algorithms are derived to find approximate optimal controllers when the system dynamics is completely unknown. Under mild conditions, the proposed data-driven off-policy algorithms converge to the optimal solution. Finally, the effectiveness and feasibility of the developed methods are validated by a practical example of spacecraft attitude control.

Sequential Quadratic Programming (SQP) for optimal control in direct numerical simulation of turbulent flow

We are honored to organize this special issue of Neural Computation and Applications, based on contributions to the Ninth International Symposium on Neural Networks (ISNN 2012) held on July 11–14, 2012, in Shenyang, China. Evaluated by the contributions and the recommendation of ISNN 2012 organizers, 22 papers were selected for the further review process with their extended form. Each paper has been reviewed thoroughly by three independent experts in related research area. We are very grateful for the hard work of the reviewers, which help to facilitate the outcome of this special issue with greatly improved quality of the contributions. Finally, 20 papers are accepted, to be introduced as follows. In brief, the contributions of this special issue can be roughly classified into three major categories: data-based control, data-based optimization, and data-based modeling. In each category, not only the theoretical foundation is analyzed, but also some prospective applications are demonstrated. In this introduction, we like to borrow some ideas from the contributions, such as hierarchical, and cluster as the subsidiary category idea. The first category consisting of 6 papers is devoted to the data-based control and applications area, by which an optimal or near-optimal control can be derived from the input and output data. The first 4 papers focus on the hot research direction, adaptive dynamic programming and reinforcement learning (ADPRL), and the remaining 2 papers relate to iterative learning control and optimal control. Derong Liu et al. develop an online algorithm based on policy iteration for continuous-time optimal control with infinite horizon cost for nonlinear systems. In the proposed method, a discount value function is employed, which is considered to be a more general case for optimal control problems. Meanwhile, without knowledge of the internal system dynamics, the algorithm can converge uniformly online to the optimal solution of the modified Hamilton– Jacobi–Bellman equation. By means of two neural networks, the algorithm is able to find suitable approximations of both the optimal control and the optimal cost. Dual iterative adaptive dynamic programming for a class of discrete-time nonlinear systems with time-delays is investigated by Qinglai Wei et al. Dual iterative ADP algorithm is introduced to obtain the optimal solutions of the optimal performance index function and control, where in each iteration, the performance index function and the system states are both updated. Convergence analysis is presented to prove the performance index function to reach D. Zhao (&) State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China e-mail: Dongbin.zhao@ia.ac.cn

This paper analyzes, theoretically and by computer simulation, the capabilities and limitations of neural networks to be used for the identification and optimal control of nonlinear dynamical systems. It is shown how neural networks can be efficiently trained to identify the forward and inverse dynamics of systems and also to work as optimal controllers which minimize some peformance measures of the system to be controlled. The performance of neural networks when applied to the optimal control of nonlinear vehicle suspensions is analyzed and compared with the performance of passive suspensions and that of active suspensions with linear (LQ) controllers designed by linearizing the nonlinear characteristics of the suspensions around the equilibrium point. It is found that nonlinear vehicle suspensions with neuro-control show better performance than suspensions controlled with conventional LQ regulators. Some issues about the implementation of neural networks to improve its convergence and generalization properties are analyzed.

Mixed Iterative Adaptive Dynamic Programming for Optimal Battery Energy Control in Microgrids

In this study, a finite‐time online optimal controller was designed for a nonlinear wheeled mobile robotic system (WMRS) with inequality constraints, based on reinforcement learning (RL) neural networks. In addition, an extended cost function, obtained by introducing a penalty function to the original long‐time cost function, was proposed to deal with the optimal control problem of the system with inequality constraints. A novel Hamilton‐Jacobi‐Bellman (HJB) equation containing the constraint conditions was defined to determine the optimal control input. Furthermore, two neural networks (NNs), a critic and an actor NN, were established to approximate the extended cost function and the optimal control input, respectively. The adaptation laws of the critic and actor NN were obtained with the gradient descent method. The semi‐global practical finite‐time stability (SGPFS) was proved using Lyapunov's stability theory. The tracking error converges to a small region near zero within the constraints in a finite period. Finally, the effectiveness of the proposed optimal controller was verified by a simulation based on a practical wheeled mobile robot model.