Linear Quadratic Cost Function Research Articles

Discrete-time neuroadaptive control using dynamic state feedback with application to vehicle motion control for intelligent vehicle highway systems

Discrete time neuro-compensated dynamic state feedback control system for lateral and longitudinal control of intelligent vehicle highway systems (IVHS) is developed. A discrete time counterpart of the continuous time non-linear IHVS model is obtained in state-space form and the controller is analysed in three stages, with and without compensation mechanisms resulting in an implementation from low to high complexity. Gain parameters of the dynamic state feedback control are optimised with respect to a minimisation of a linear quadratic cost function. The weight convergence of the neuro-compensation algorithm is established in discrete time Lyapunov sense via a graphical method. The performance enhancement of each design stage of the controller is presented and compared with the aid of computer simulations.

Frequency domain iterative feedforward/feedback tuning for MIMO ANVC

A new gradient estimation method is proposed that relies on efficient computation of the negative gradient of the average linear quadratic cost function completely in the frequency domain. Based on the proposed theory, a new iterative tuning method is developed to solve linear multi-input multi-output Active Noise/Vibration Control problems. Compared with published iterative tuning methods, the new method has the added advantage that the number of experiments per iteration is reduced to one. Combined with the other advantage of relatively simple controller structures, the method is suitable for realtime implementation as an adaptive controller.

Supervisory Multiple-Model Approach to Multivariable Lambda and Torque Control of SI Engines

The problem of simultaneous air-fuel ratio regulation and torque tracking in a spark ignition engine with electronic throttle control is considered. The proposed methodology involves the use of a set of piecewise-affine models to represent the nonlinear engine dynamics. These models are the basis of a supervisory multiple-model control scheme, which, in its simplest form, consists in switching among the predefined bank of controllers. In the following a monitoring signal generator is driven by a bank of observers, and a supervisor ensures the robustness of the switching scheme. An optimal linear-quadratic cost function enables the trade-off between emissions performance and drivability to be adjusted. Simulation results using the data obtained from a vehicle with a 5.3L V8 engine on Federal Test Procedure (FTP) driving cycles are presented, with a nonlinear regression model of the engine identified from the FTP data. The results indicate that both tight lambda regulation and fast torque tracking are possible using the proposed designs.

LQ suboptimal decentralised controllers with disturbance rejection property for hierarchical systems

This article is concerned with decentralised output regulation of hierarchical systems subject to input and output disturbances. It is assumed that the disturbance can be represented as the output of an autonomous linear time invariant (LTI) system with an unknown initial state. The primary objective is to design a decentralised controller with the property that not only does it reject the degrading effect of the disturbance on the output (to achieve a satisfactory steady-state performance), it also results in a small linear quadratic (LQ) cost function (implying a good transient behaviour). To this end, the underlying problem is treated in two phases. In the first step, a number of modified systems are defined in terms of the original system. The problem of designing an LQ centralised controller which stabilises all the modified systems and rejects the disturbance in the original system is considered, and it is shown that this centralised controller can be found efficiently by solving a linear matrix inequality (LMI) problem. In the second step, a method recently presented in the literature is exploited to decentralise the designed centralised controller. It is shown that the obtained controller satisfies the prescribed design specifications including disturbance rejection. Finally, in a more pragmatic context, the system is assumed to be subject to input delay, and a robustness analysis is carried out accordingly. Simulation results elucidate the efficacy of the proposed control law.

Time-Multiplied Guaranteed Cost Control of Linear Delay Systems

This paper investigates the design of guaranteed cost controllers for a class of linear systems with a state delay using a time-multiplied linear quadratic cost function. Based on delay-dependent and delay-independent stability criteria, guaranteed cost controllers can be constructed via solutions to linear matrix inequalities (LMIs) such that the resulting closed-loop system is stable and a specified time-multiplied linear integral-quadratic cost function has an upper bound. By the cone complementary linearization method, delay-dependent state feedback controllers can be derived in terms of LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Optimal guaranteed cost control for fuzzy descriptor systems with time-varying delay

Based on the delay-independent rule, the problem of optimal guaranteed cost control for a class of Takagi-Sugeno (T-S) fuzzy descriptor systems with time-varying delay is studied. A linear quadratic cost function is considered as the performance index of the closed-loop system. Sufficient conditions for the existence of guaranteed cost controllers via state feedback are given in terms of linear matrix inequalities (LMIs), and the design of an optimal guaranteed cost controller can be reduced to a convex optimization problem. It is shown that the designed controller not only guarantees the asymptotic stability of the closed-loop fuzzy descriptor delay system, but also provides an optimized upper bound of the guaranteed cost. At last, a numerical example is given to illustrate the effectiveness of the proposed method and the perfect performance of the optimal guaranteed cost controller.

An optimal linear-quadratic digital tracker for analog neutral time-delay systems

In this paper, an optimal hybrid tracking control problem for continuous neutral time-delay systems is formulated and studied. An optimal linear integral quadratic cost function that has a high-gain property is used for tracking control specification. Two interpolation methods are applied to directly convert the original analog neutral time-delay system into an equivalent digital retarded time-delay system, and meanwhile convert the continuous-time quadratic cost function into a discretized form. Then, an extended state vector is constructed for an associate extended discrete-time optimal control problem without time delay. Using the standard discrete-time linear-quadratic optimal control theory and an indirect digital redesign technique with a predictive feature, an effective digital tracker is designed for the original analog neutral time-delay system. An example is finally given for illustrating the effectiveness of the new tracker design method.

Fuzzy guaranteed cost control for nonlinear systems with time-varying delay

This paper focuses on the problem of guaranteed cost control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delayed state. A linear quadratic cost function is considered as a performance index of the closed-loop fuzzy system. Then, the guaranteed cost control of the closed-loop fuzzy system is discussed, and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer-based output feedback. When these conditions, which are given in terms of the feasibility of linear matrix inequalities (LMIs), are satisfied, the designed state feedback controller and observer-based controller gain matrices can be obtained via a convex optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper.

MODEL PREDICTIVE CONTROL OF SYSTEMS WITH COMMUNICATION CONSTRAINTS

This paper addresses the problem of the on-line scheduling of a limited communication resource in order to optimize the control performance. A multivariable linear system with communication constraints is modeled in the Mixed Logical Dynamical (MLD) framework. The system is controlled using a Model Predictive Controller (MPC), which computes, at each sampling period, the appropriate control values and network allocation. The performance of the controlled system is evaluated using a Linear-Quadratic cost function. At each step, the MPC needs to solve an optimization problem, including logic constraints. The translation of this problem into the Mixed Integer Quadratic Programming (MIQP) formulation is described. Finally, using a numerical example, the relationship between the state variables of the plant and the resultant allocation of the communication resource is investigated.

Optimal Regulator for Quadratic Systems with Linear Input and Its Application to Terpolymerization Reactor Control Design

The paper presents the optimal regulator for a state of a quadratic system with linear control input and quadratic cost function. The result is derived by means of the duality principle and then proved using the maximum principle. The general scheme for obtaining the optimal regulator in case of a polynomial system with linear control input and quadratic criterion is announced. The designed optimal regulator is applied to solution of the optimal control problem for a terpolymerization reactor and compared to the best linear filter available for the linearized model. The simulation results show a definitive advantage of the designed optimal regulator with respect to the criterion and regulated state values.

On Dynamic Output Feedback Guaranteed Cost Control of Uncertain Discrete-Delay Systems: LMI Optimization Approach

In this paper, we consider a design problem of dynamic output feedback controller for guaranteed cost stabilization of discrete-delay systems with norm-bounded time-varying parameter uncertainties. A linear-quadratic cost function is considered as a performance measure for the closed-loop system. Based on the Lyapunov second method, several stability criteria for the existence of the controller are derived in terms of linear matrix inequalities (LMIs). The solutions of the LMIs can be obtained easily using existing efficient convex optimization techniques. A numerical example is given to illustrate the proposed method.

A design of self‐tuning pole‐assignment control systems based on minimizing quadratic cost functions

AbstractThere are numerous studies of the design of self‐tuning control (STC) systems for linear nonminimum‐phase systems. A wide variety of existing methods on designing STC systems are conceptually classified into two groups. One is based on minimization of an error criterion, and the other on pole assignment of the closed‐loop system. On the other hand, in order to guarantee the tracking property for the reference signals, an internal model which corresponds to the reference signals must be inserted into the control system based on the internal model principle. However, the variance of the control error signal may become large on inserting the internal model, because stochastic noise may be amplified. In this paper, a design method for self‐tuning pole‐assignment control systems with internal models is proposed based on minimizing the linear quadratic cost function. The newly proposed control scheme has the feature that the variance of the stochastic noise in the control system is reduced owing to the minimum variance control scheme, and also the tracking property with respect to the reference signal is assured owing to the internal model. The proposed control scheme is numerically evaluated in some simulation examples. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 144(1): 50–57, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10120

Application of iterative learning control to an exothermic semibatch chemical reactor

Focuses on the temperature control of a semibatch chemical reactor used for fine chemicals production. Such a reactor is equipped with a heating/cooling system composed of different thermal fluids. Without extensive modeling investigations, a feedback-feedforward control strategy is proposed for ensuring the tracking performance of the desired temperature profile. Such a strategy is derived from a family of the iterative learning control (ILC) algorithms named batch model predictive control (BMPC). Learning is achieved without requiring a detailed knowledge of the system, which may be affected by unknown but repetitive disturbances. The learning control solution is based on the minimization of a linear quadratic cost function. The synthesis of the proposed strategy is studied, and improvements of the algorithm features are proposed. First, guaranteed convergence of the algorithm is illustrated in a few experimental runs. Second, some practical considerations for the removal of high-frequency disturbance effects are outlined to improve the achieved performance. Third, a robust supervisory control procedure is employed to choose the right fluid and to reduce the superfluous fluid changeovers, mainly when different fluids are available. Finally, experimental results are presented to illustrate the practical appeal and effectiveness of the proposed scheme.

最小分散を考慮したセルフチューニング極配置制御系の一設計

There are numerous studies of the design of self-tuning control (STC) systems for linear nonminimum-phase systems. A wide variety of existing methods on designing STC systems are conceptually classified into two groups. One is based on minimization of an error criterion, and the other on pole assignment of the closed-loop system. On the other hand, in order to guarantee the tracking property for the reference signals, an internal model which corresponds to the reference signals must be inserted into the control system based on the internal model principle. However, the variance of the control error signal may become large on inserting the internal model, because stochastic noise may be amplified. In this paper, a design method for self-tuning pole-assignment control systems with internal models is proposed based on minimizing the linear quadratic cost function. The newly proposed control scheme has the feature that the variance of the stochastic noise in the control system is reduced owing to the minimum variance control scheme, and also the tracking property with respect to the reference signal is assured owing to the internal model. The proposed control scheme is numerically evaluated in some simulation examples. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 144(1): 50–57, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10120

A feedback scheduler for real-time controller tasks

The problem studied in this paper is how to distribute computing resources over a set of real-time control loops in order to optimize the total control performance. Two subproblems are investigated: how the control performance depends on the sampling interval, and how a recursive resource allocation optimization routine can be designed. Linear quadratic cost functions are used as performance indicators. Expressions for calculating their dependence on the sampling interval are given. An optimization routine, called a feedback scheduler, that uses these expressions is designed.

An LMI approach to output-feedback-guaranteed cost control for uncertain time-delay systems

This paper considers the problem of output-feedback-guaranteed cost controller design for uncertain time-delay systems. The uncertainty in the system is assumed to be norm-bounded and time-varying. The time-delay is allowed to enter the state and the measurement equations. A linear quadratic cost function is considered as a performance measure for the closed-loop system. Necessary and sufficient conditions are provided for the construction of a guaranteed cost controller. These conditions are given in terms of the feasibility of LMIs which depend on a positive definite matrix and a scaling variable. A numerical algorithm is developed to search for a full order dynamic output-feedback controller which minimizes the cost bound. Copyright © 2000 John Wiley & Sons, Ltd.

Synthesis of minimax optimal controllers for uncertain time-delay systems with structured uncertainty

This paper is concerned with the design of robust state feedback controllers for a class of uncertain time-delay systems. The uncertainty is assumed to satisfy a certain integral quadratic constraint. The controller proposed is a minimax optimal controller in the sense that it minimizes the maximum value of a corresponding linear quadratic cost function over all admissible uncertainties. The controller leads to an absolutely stable closed loop uncertain system and is constructed by solving a finite dimensional parameter-dependent algebraic Riccati equation.

Guaranteed cost control of uncertain discrete systems with delays

In this paper, we address the problems of robust performance analysis and control synthesis for a class of discrete-time systems with parameter uncertainty and unknown state-delay. The parameter uncertainty is real time-varying normbounded and the state-delay is a constant within a prescribed interval. For the robust performance analysis problem, we adopt an appropriate notion of robust stability for discrete-time uncertain time-delay systems and show that this notion guarantees an upper bound on a linear quadratic cost function. For the control synthesis problem, we show that a robust state-feedback controller can be constructed to render the closed-loop system robustly stable while guaranteeing a prescribed level of performance. The developed results are expressed in terms of algebraic matrix inequalities. A numerical example is presented to illustrate the theory.

OPTIMAL CONTROL FOR TWO‐DIMENSIONAL LINEAR SYSTEMS WITH VARIABLE COEFFICIENTS

An optimal control method for two‐dimensional (2‐D) linear systems with variable coefficients and free boundary conditions in Roesser's model is proposed in this paper. Based on Roesser's model, an equivalent general 1‐D model of the 2‐D system is presented, and the problem of minimizing a 2‐D linear quadratic (LQ) cost function is solved for the case where complete state information is available. The solution is obtained by using the proposed dynamic programming in 1‐D descriptor form to solve the Riccati equation and then arriving at the optimal control law and minimum cost. The proposed control methodology can be applied to discrete‐time models of systems described by partial differential equations and can also be used in the field of signal processing.

Direct Controller Adjustment by On-Line Performance Assessment

This paper introduces a mechanism for assessment of local optimality of closed-loop performance. The basis of this result is the estimation of the first and second derivatives of a cost function with respect to the controller parameters. The criterion adopted to measure the system performance is the linear quadratic cost function, in the time domain, although its derivatives are obtained in the frequency domain via spectral analysis of closed-loop signals.These estimates of first and second derivatives of the cost function are also valuable for computing appropriate directions for tuning the controller parameters. Even though the derivatives are computed in the frequency domain, the actual cost function is computed with time-domain measurements taken along the tuning directions. The tuning scheme can be direct (model free) or based on a nonparametric model of the plant. Moreover, this scheme includes a mechanism for guaranteeing stability of the closed-loop system.