Stability of singular networked control systems with control constraint

Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for delay-independent stability and delay-dependent stability of singular networked control systems are derived and transformed to a feasibility problem of linear matrix inequality formulation, which can be solved by the Matlab LMI toolbox, and the feasible solutions provide the maximum allowable delay bound that makes the system stable. A numerical example is provided, which shows that the analysis method is valid and the stability criteria are feasible.

RECOVERY A POSTERIORI ERROR ESTIMATES FOR GENERAL CONVEX ELLIPTIC OPTIMAL CONTROL PROBLEMS SUBJECT TO POINTWISE CONTROL CONSTRAINTS

Superconvergence and recovery a posteriori error estimates of the finite element ap- proximation for general convex optimal control problems are investigated in this paper. We obtain the superconvergence properties of finite element solutions, and by using the superconvergence results we get recovery a posteriori error estimates which are asymptotically exact under some regularity conditions. Some numerical examples are provided to verify the theoretical results.

Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.

Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters

A dynamics-based adaptive control approach is proposed for a planar dual-arm space robot in the presence of closed-loop constraints and uncertain inertial parameters of the payload. The controller is capable of controlling the po- sition and attitude of both the satellite base and the payload grasped by the manipulator end effectors. The equations of motion in reduced-order form for the constrained system are derived by incorporating the constraint equations in terms of accelerations into Kane＇s equations of the unconstrained system. Model analysis shows that the resulting equations perfectly meet the requirement of adaptive controller design. Consequently, by using an indirect approach, an adaptive control scheme is proposed to accomplish position/attitude trajectory tracking control with the uncertain parameters be- ing estimated on-line. The actuator redundancy due to the closed-loop constraints is utilized to minimize a weighted norm of the joint torques. Global asymptotic stability is proven by using Lyapunov＇s method, and simulation results are also presented to demonstrate the effectiveness of the proposed approach.

Multi-model predictive control with local constraints based on model switching

Because model switching system is a typical form of Takagi-Sugeno（T-S） model which is an universal approximator of continuous nonlinear systems, we describe the model switching system as mixed logical dynamical （MLD） system and use it in model predictive control （MPC） in this paper. Considering that each local model is only valid in each local region,we add local constraints to local models. The stability of proposed multi-model predictive control （MMPC） algorithm is analyzed, and the performance of MMPC is also demonstrated on an inulti-multi-output（MIMO） simulated pH neutralization process.

High-Speed Trains Automatic Operation with Protection Constraints: A Resilient Nonlinear Gain-based Feedback Control Approach

This paper addresses the control design for automatic train operation of high-speed trains with protection constraints.A new resilient nonlinear gain-based feedback control approach is proposed,which is capable of guaranteeing,under some proper non-restrictive initial conditions,the protection constraints control raised by the distance-to-go(moving authority)curve and automatic train protection in practice.A new hyperbolic tangent function-based model is presented to mimic the whole operation process of high-speed trains.The proposed feedback control methods are easily implementable and computationally inexpensive because the presence of only two feedback gains guarantee satisfactory tracking performance and closed-loop stability,no adaptations of unknown parameters,function approximation of unknown nonlinearities,and attenuation of external disturbances in the proposed control strategies.Finally,rigorous proofs and comparative simulation results are given to demonstrate the effectiveness of the proposed approaches.

Best Tracking Performance under Plant Uncertainty and Control Energy Constraint

This paper has investigated best tracking performance for linear feedback control systems in the case that plant uncertainty and control effort need to be considered simultaneously. Firstly, an average integral square criterion of the tracking error and the plant input energy over a class of additive model errors is defined. Then, utilizing spectral factorization to minimize the performance index, we obtain an optimal controller design method, and furthermore study optimal tracking performance under plant uncertainty and control energy constraint. The results can be used to evaluate optimal average tracking performance and control energy in designing practical control systems.

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.

New model reference adaptive control with input constraints

A new scheme of adaptive control is proposed for a class of linear time-invariant（ LTI） dynamical systems,especially in aerospace,with matched parametric uncertainties and input constraints. Based on a typical and conventional direct model reference adaptive control scheme,various modifications have been employed to achieve the goal. ＂C omposite model reference adaptive control＂of higher performance is seam-lessly combined with ＂positive μ-mod＂,which consequently results in a smooth tracking trajectory despite of the input constraints. In addition,bounded-gain forgetting is utilized to facilitate faster convergence of parameter estimates. The stability of the closed-loop systemcan be guaranteed by using Lyapunov theory.The merits and effectiveness of the proposed method are illustrated by a numerical example of the longitudinal dynamical systems of a fixed-wing airplane.

A Nonlinear Flow Control Scheme Under Capacity Constraints

We present a nonlinear flow control scheme based on a buffer management model with physical constraints. It extends previous result of Pitsillides et al. in [6] by improving the queue length regulation for better service of network traffics. Besides a single node system, we also address the decentralized control of many cascaded nodes. The proposed discontinuous controller asymptotically regulates the buffer queue length at the output port of a router/switch to a constant reference value, under unknown time varying interfering traffics and saturation constraints on control input and states. Its continuous approximation achieves practical regulation with an ultimate bound on the regulation error tunable by a design parameter.

NECESSARY CONDITIONS FOR OPTIMAL CONTROLS OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES INVOLVING STATE CONSTRAINT

This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.

Feasibility analysis and online adjustment of constraints in model predictive control integrated with soft sensor

Feasibility analysis of soft constraints for input and output variables is critical for model predictive control(MPC).When encountering the infeasible situation, some way should be found to adjust the constraints to guarantee that the optimal control law exists. For MPC integrated with soft sensor, considering the soft constraints for critical variables additionally makes it more complicated and difficult for feasibility analysis and constraint adjustment. Therefore, the main contributions are that a linear programming approach is proposed for feasibility analysis, and the corresponding constraint adjustment method and procedure are given as well. The feasibility analysis gives considerations to the manipulated, secondary and critical variables, and the increment of manipulated variables as well. The feasibility analysis and the constraint adjustment are conducted in the entire control process and guarantee the existence of optimal control. In final, a simulation case confirms the contributions in this paper.

Multimodel-based flight control system reconfiguration control in the presence of input constraints

In this paper,an active fault accommodate strategy is proposed for the plant in the presence of actuator fault and input constraints,which is a combination of a direct adaptive control algorithm with multiple model switching.The μ-modification is introduced in the model reference architecture to construct the adaptive controller.The proof of stability is based on the candidate Lyapunov function,while appropriate switching of multiple models guarantees asymptotic tracking of the system states and the boundedness of all signals.Simulation results illustrate the efficiency of the proposed method.

OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS

The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered.The optimal solutions are obtained.In addition,their approximating problems are also studied.

A Maximum Principle for Smooth Infinite Horizon Optimal Control Problems with State Constraints and with Terminal Constraints at Infinity

Necessary conditions for optimality are proved for smooth infinite horizon optimal control problems with unilateral state constraints (pathwise constraints) and with terminal conditions on the states at the infinite horizon. The aim of the paper is to obtain strong necessary conditions including transversality conditions at infinity, which in many cases lead to a set of candidates for optimality containing only a few elements, similar to what is the case in finite horizon problems. However, strong growth conditions are needed for the results to hold.

An improved approach to H-two control withregional stability constraints

This paper presents an improved method for H-two control with regional stability constraints for the closedloop system. The controller is given by the convex combination of a set of fixed gains. Both continuous and discrete-time systems in a known polytopic domain are investigated. New LMI-based sufficient conditions for the existence of parameterdependent Lyapunov functions are proposed. Numerical examples are given to show the proposed conditions provide useful and less conservative results for the problems of H-two control with regional stability constraints.

State Space Model Predictive Control of an Aerothermic Process with Actuators Constraints

This paper investigates State Space Model Predictive Control (SSMPC) of an aerothermic process. It is a pilot scale heating and ventilation system equipped with a heater grid and a centrifugal blower, fully connected through a data acquisition system for real time control. The interaction between the process variables is shown to be challenging for single variable controllers, therefore multi-variable control is worth considering. A multi-variable state space model is obtained from on-line experimental data. The controller design is translated into a Quadratic Programming (QP) problem, in which a cost function subject to actuators linear inequality constraints is minimized. The outcome of the experimental results is that the main control objectives, such as set-point tracking and perturbations rejection under actuators constraints, are well achieved for both controlled variables simultaneously.

Robust Fuzzy Tracking Control for Nonlinear Networked Control Systems with Integral Quadratic Constraints

This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.