Closed‐form solution to finite‐horizon suboptimal control of nonlinear systems

Finite‐horizon optimal control of input‐affine nonlinear systems with fixed final time is considered in this study. It is first shown that the associated Hamilton–Jacobi–Bellman partial differential equation to the problem is reducible to a state‐dependent differential Riccati equation after some approximations. With a truncation in the control equation, a near optimal solution to the problem is obtained, and the global onvergence properties of the closed‐loop system are analyzed. Afterwards, an approximate method, called Finite‐horizon State‐Dependent Riccati Equation (Finite‐SDRE), is suggested for solving the differential Riccati equation, which renders the origin a locally exponentially stable point. The proposed method provides online feedback solution for controlling different initial conditions. Finally, through some examples, the performance of the resulting controller in finite‐horizon control is analyzed. Copyright © 2014 John Wiley & Sons, Ltd.     

Control of near‐grazing dynamics and discontinuity‐induced bifurcations in piecewise‐smooth dynamical systems

This paper develops a rigorous control paradigm for regulating the near‐grazing bifurcation behavior of limit cycles in piecewise‐smooth dynamical systems. In particular, it is shown that a discrete‐in‐time linear feedback correction to a parameter governing a state‐space discontinuity surface can suppress discontinuity‐induced fold bifurcations of limit cycles that achieve near‐tangential intersections with the discontinuity surface. The methodology ensures a persistent branch of limit cycles over an interval of parameter values near the critical condition of tangential contact that is an order of magnitude larger than that in the absence of control. The theoretical treatment is illustrated with a harmonically excited damped harmonic oscillator with a piecewise‐linear spring stiffness as well as with a piecewise‐nonlinear model of a capacitively excited mechanical oscillator. Copyright © 2009 John Wiley & Sons, Ltd.     

Linear‐Quadratic Optimal Control Problems for Mean‐Field Stochastic Differential Equations with Jumps

In this paper, we study a linear‐quadratic optimal control problem for mean‐field stochastic differential equations driven by a Poisson random martingale measure and a one‐dimensional Brownian motion. Firstly, the existence and uniqueness of the optimal control is obtained by the classic convex variation principle. Secondly, by the duality method, the optimality system, also called the stochastic Hamilton system which turns out to be a linear fully coupled mean‐field forward‐backward stochastic differential equation with jumps, is derived to characterize the optimal control. Thirdly, applying a decoupling technique, we establish the connection between two Riccati equations and the stochastic Hamilton system and then prove the optimal control has a state feedback representation.     

Linear‐Quadratic Optimal Control Problem for Partially Observed Forward‐Backward Stochastic Differential Equations of Mean‐Field Type

This paper is concerned with the linear‐quadratic optimal control problem for partially observed forward‐backward stochastic differential equations (FBSDEs) of mean‐field type. Based on the classical spike variational method, backward separation approach as well as filtering technique, we first derive the necessary and sufficient conditions of the optimal control problem with the non‐convex domain. Nextly, by means of the decoupling technique, we obtain two Riccati equations, which are uniquely solvable under certain conditions. Also, the optimal cost functional is represented by the solutions of the Riccati equations for the special case.     

Output Feedback H∞ Control for Discrete‐time Mean‐field Stochastic Systems

This paper is to consider dynamic output feedback H_∞ control of mean‐field type for stochastic discrete‐time systems with state‐ and disturbance‐dependent noise. A stochastic bounded real lemma (SBRL) of mean‐field type is derived. Based on the SBRL, a sufficient condition with the form of coupled nonlinear matrix inequalities is derived for the existence of a stabilizing H_∞ controller. Moreover, a numerical example is given to examine the effectiveness of the theoretical results.     

H∞ Control for Continuous‐Time Mean‐Field Stochastic Systems

An H_∞‐type control is considered for mean‐field stochastic differential equations (SDEs) in this paper. A stochastic bounded real lemma (SBRL) is proved for mean‐field stochastic continuous‐time systems with state‐ and disturbance‐dependent noise. Based on SBRL, a sufficient condition is given for the existence of a stabilizing H_∞ controller in terms of coupled nonlinear matrix inequalities.     

Mean‐field games for multiagent systems with multiplicative noises

This paper studies mean‐field games for multiagent systems with control‐dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal control problem subject to consistent mean‐field approximations. The set of decentralized strategies is further shown to be an ε‐Nash equilibrium. For the integrator multiagent systems, we design a set of ε‐Nash strategies by exploiting the convexity property of the limiting problem. It is shown that under the mild conditions, all the agents achieve mean‐square consensus.     

INTERNET‐BASED REAL‐TIME CONTROL ARCHITECTURES WITH TIME‐DELAY/PACKET‐LOSS COMPENSATION

The main objective of this paper is to demonstrate the feasibility of Internet‐based real‐time control. A novel client/server‐based architecture for Internet‐based supervisory control with a Common Gateway Interface/Hyper Text Markup Language (CGI/HTML) interface is presented. A real‐time operating environment was established for closed‐loop control over Ethernet. We conceived of an autoregressive (AR) prediction scheme and a novel compensation algorithm to compensate for network‐induced time delays and data‐packet losses simultaneously. We constructed an open‐loop unstable ball magnetic‐levitation (maglev) setup as a test bed to validate the two proposed control architectures. Experimental results proved the feasibility of Internet‐based real‐time control and verified the effectiveness of the proposed time‐delay/packet‐loss compensation algorithm in networked feedback control systems.     

Optimal Control Problem for Risk‐Sensitive Mean‐Field Stochastic Delay Differential Equation with Partial Information

This paper deals with the risk‐sensitive control problem for mean‐field stochastic delay differential equations (MF‐SDDEs) with partial information. Firstly, under the assumptions that the control domain is not convex and the value function is non‐smooth, we establish a stochastic maximum principle (SMP). Then, by means of Itô's formula and some continuous dependence, we prove the existence and uniqueness results for another type of MF‐SDDEs. Meanwhile, the verification theorem for the MF‐SDDEs is obtained by using a clever construction of the Hamiltonian function. Finally, based on our verification theorem, a linear‐quadratic system is investigated and the optimal control is also derived by the stochastic filtering technique.     

Comparison of image reconstruction by using near‐field and far‐field data for an imperfect conductor

Image reconstruction by using near‐field and far‐field data for an imperfectly conducting cylinder is investigated. A conducting cylinder of unknown shape and conductivity scatters the incident wave in free space and the scattered near and far fields are measured. By using measured fields, the imaging problem is reformulated into an optimization problem and solved by the genetic algorithm. Numerical results show that the convergence speed and final reconstructed results by using near‐field data are better than those obtained by using far‐field data. This work provides both comparative and quantitative information. © 2001 John Wiley & Sons, Inc. Int J RF and Microwave CAE 11: 69–73, 2001.     

Design of a low‐cost 1‐20 GHz magnetic near‐field probe with FR‐4 printed circuit board

An ultra‐wideband magnetic near‐field probe based on a conventional low‐cost four layers of FR‐4 printed circuit board is proposed in this article. It can be used to measure the magnetic near‐field strength from RF magnetic sources or electronic devices for EMI conformance test. The operating frequency of the probe is from 1 GHz up to 20 GHz. The probe is constructed based on a coplanar waveguide and stripline with a short‐end loop. The probe dimension is 10 mm × 25 mm × 0.6 mm. The prototype probe is electric field‐shield structure and has a very high unwanted electric field suppression ratio about 17.7 dB. The probe calibration factor from the simulation agrees well with the calibration factor computed from the measurement. The average probe factor is 38.8 dBS/m and probe sensitivity is 47.4 dB μ A/m.     

Robust event‐triggered model predictive control for cyber‐physical systems under denial‐of‐service attacks

This paper investigates the resilient control problem for constrained continuous‐time cyber‐physical systems subject to bounded disturbances and denial‐of‐service (DoS) attacks. A sampled‐data robust model predictive control law with a packet‐based transmission scheduling is taken advantage to compensate for the loss of the control data during the intermittent DoS intervals, and an event‐triggered control strategy is designed to save communication and computation resources. The robust constraint satisfaction and the stability of the closed‐loop system under DoS attacks are proved. In contrast to the existing studies that guarantee the system under DoS attacks is input‐to‐state stable, the predicted input error caused by the system constraints can be dealt with by the input‐to‐state practical stability framework. Finally, a simulation example is performed to verify the feasibility and efficiency of the proposed strategy.     

Discrete‐Valued Model Predictive Control Using Sum‐of‐Absolute‐Values Optimization

In this paper, we propose a new design method of discrete‐valued model predictive control for continuous‐time linear time‐invariant systems based on sum‐of‐absolute‐values (SOAV) optimization. The finite‐horizon discrete‐valued control design is formulated as an SOAV optimal control, which is an expansion of L¹ optimal control. It is known that under the normality assumption, the SOAV optimal control exists and takes values in a fixed finite alphabet set if the initial state lies in a subset of the reachable set. In this paper, we analyze the existence and discreteness property for systems that do not necessarily satisfy the normality assumption. Then, we extend the finite‐horizon SOAV optimal control to infinite‐horizon model predictive control (MPC). We give sufficient conditions for the recursive feasibility and the stability of the MPC‐based feedback system in the presence of bounded noise. Simulation results show the effectiveness of the proposed method.     

Modeling and control of an airbrake electro‐hydraulic smart actuator

In this paper, an accurate model of an airbrake electro‐hydraulic smart actuator is obtained by physical considerations, and then different control strategies (variable‐gain proportional control, PT₁ control with switching integrator, and second order sub‐optimal sliding mode control) are proposed and analyzed. This application is innovative in the avionic field, and is one of the first attempts to realize a fly‐by‐wire system for airbrakes, oriented to its immediate employment and installation on current aircraft. The project was carried on with the participation of the Italian Ministry of Defense, and was commissioned to MAG, a leading provider of integrated systems and aviation services for aerospace. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Mean‐field backward stochastic differential equation with non‐Lipschitz coefficient

This paper establishes a new existence and uniqueness result of a solution for one dimensional mean‐field backward stochastic differential equation (MFBSDE), where its coefficient is weaker than the classical Lipschitz case. An example is given to illustrate its applicability. This new solution will provide a key tool for studying mean‐field control problems.     

Tracking control for sampled‐data systems with uncertain time‐varying sampling intervals and delays

In this paper, a solution to the approximate tracking problem of sampled‐data systems with uncertain, time‐varying sampling intervals and delays is presented. Such time‐varying sampling intervals and delays can typically occur in the field of networked control systems. The uncertain, time‐varying sampling and network delays cause inexact feedforward, which induces a perturbation on the tracking error dynamics, for which a model is presented in this paper. Sufficient conditions for the input‐to‐state stability (ISS) of the tracking error dynamics with respect to this perturbation are given. Hereto, two analysis approaches are developed: a discrete‐time approach and an approach in terms of delay impulsive differential equations. These ISS results provide bounds on the steady‐state tracking error as a function of the plant properties, the control design and the network properties. Moreover, it is shown that feedforward preview can significantly improve the tracking performance and an online extremum seeking (nonlinear programming) algorithm is proposed to online estimate the optimal preview time. The results are illustrated on a mechanical motion control example showing the effectiveness of the proposed strategy and providing insight into the differences and commonalities between the two analysis approaches. Copyright © 2009 John Wiley & Sons, Ltd.     

FPGA‐based adaptive dynamic sliding‐mode neural control for a brushless DC motor

In the adaptive neural control design, since the number of hidden neurons is finite for real‐time applications, the approximation errors introduced by the neural network cannot be inevitable. To ensure the stability of the adaptive neural control system, a switching compensator is designed to dispel the approximation error. However, it will lead to substantial chattering in the control effort. In this paper, an adaptive dynamic sliding‐mode neural control (ADSNC) system composed of a neural controller and a fuzzy compensator is proposed to tackle this problem. The neural controller, using a radial basis function neural network, is the main controller and the fuzzy compensator is designed to eliminate the approximation error introduced by the neural controller. Moreover, a proportional‐integral‐type adaptation learning algorithm is developed based on the Lyapunov function; thus not only the system stability can be guaranteed but also the convergence of the tracking error and controller parameters can speed up. Finally, the proposed ADSNC system is implemented based on a field programmable gate array chip for low‐cost and high‐performance industrial applications and is applied to control a brushless DC (BLDC) motor to show its effectiveness. The experimental results demonstrate the proposed ADSNC scheme can achieve favorable control performance without encountering chattering phenomena. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

On Near‐controllability of Discrete‐time Upper‐triangular Bilinear Systems with Applications to Controllability

Near‐controllability is defined for those systems that are uncontrollable but have a large controllable region. It is a property of nonlinear control systems introduced recently, and it has been demonstrated on two classes of discrete‐time bilinear systems. This paper studies near‐controllability of discrete‐time upper‐triangular bilinear systems, which are uncontrollable and are more general than the two classes mentioned. A necessary and sufficient condition for the systems in dimension two to be nearly controllable is presented, which covers the existing results. For the systems with high dimensions, necessary conditions and sufficient conditions of near‐controllability are provided, which generalize the existing results. In particular, the obtained near‐controllability results are applied to controllability of discrete‐time bilinear systems. An example also is given to demonstrate the effectiveness, which shows that the controllability problems of discrete‐time bilinear systems can be solved by near‐controllability.     

NN‐Based Output‐Feedback Control for Stochastic Nonlinear Systems with Unknown Control Directions

This paper addresses the neural network‐based output‐feedback control problem for a class of stochastic nonlinear systems with unknown control directions. The restrictions on the drift and diffusion terms are removed and the conditions on unknown control directions are relaxed. By introducing a proper coordinate transformation, and combining dynamic surface control (DSC) technique with radial basis function neural network (RBF NN) approximation approach, we construct an adaptive output‐feedback controller to guarantee the closed‐loop system to be mean square semi‐globally uniformly ultimately bounded (M‐SGUUB). A simulation example demonstrates the effectiveness of the proposed scheme.     

A STABLE ON‐LINE SELF‐TUNING OPTIMAL PID CONTROLLER FOR A CLASS OF UNKNOWN SYSTEMS

In this paper, a novel self‐tuning method of optimal PID control laws is proposed for both continuous‐time systems and discrete‐time systems. The controlled plant is assumed to be unknown except the system order (or system delay) and the direction of transmitting control input. Through the minimization of PID gains subject to the Lyapunov stability based reaching condition, the tuning of the three PID control gains is transformed to solve the inequality constraint optimization problem. An unknown SISO nonlinear system subject to a unit step input, and the tracking control problem of the piezoelectric actuator (PZA) with unknown dynamics are simulated. The simulation results show that the excellent tracking performance can be achieved.