Simplified parameter adaptive control

A simple parameter adaptive controller design methodology is introduced in which steady-state servo tracking properties provide the major control objective. This is achieved without cancellation of process zeros and hence the underlying design can be applied to non-minimum phase systems. As with other self-tuning algorithms, the design (user specified) polynomials of the proposed algorithm define the performance capabilities of the resulting controller. However, with the appropriate definition of these polynomials, the synthesis technique can be shown to admit different adaptive control strategies, e.g. self-tuning PID and self-tuning pole-placement controllers. The algorithm can therefore be thought of as an embodiment of other self-tuning design techniques. The performances of some of the resulting controllers are illustrated using simulation examples and the on-line application to an experimental apparatus.     

A state space self-tuning controller with integral action

The paper is concerned with the problem of designing a state space self-tuning controller with integral action for a class of unknown linear stochastic systems. The observer form of the innovations model of the system is used along with a single-stage quadratic-in-state-and-control performance index which includes a cross-weighting between system states and inputs. This results in a proportional estimated state plus integral output (P + I) controller in an incremental form. While it is analogous to the LQG-theory-based optimal adaptive controller in structure, computational simplification is achieved by the choice of a single-stage performance index and a direct estimation of the state estimator gain matrix. The new controller has the advantages of being applicable to both single-input/single output (SISO) and multi-input/multi-output (MIMO) minimum phase and non-minimum phase systems. The results are illustrated numerically through two simulation examples.     

Generalized minimum variance control law revisited

The generalized minimum variance control law is employed in many of the most successful self-tuning control schemes. However, the control law was derived by using a single-stage cost function where a conditional expectation operator was employed. This has limited our understanding of the operation of the control law and resulted in certain operational disadvantages. By rederiving the controller using a normal LQG approach but with a cost function of the same basic form, some of these deficiencies are mitigated. Moreover, the reason that the controller has poor stability characteristics on non-minimum phase systems becomes apparent and it is shown that the magnitude of the error weighting term must be severely restricted in some problems if stability is to be maintained. Thus it may not be possible to limit error variance to the desired extent.     

A decoupling pole placement self-tuning controller for a class of multivariable processes

This paper describes a new multivariable self-tuning controller that specifically handles different time delays between each of the input-output pairs (multiple delays), and deals with unknown or varying time delay (variable dead time compensation) without requiring an explicit estimate of each delay. The new algorithm can control unstable and/or non-minimum phase processes; it eliminates both set-point and load offsets without having to maintain integral action continuously; it decouples the loops, both dynamically and at steady state. The effective decoupling algorithm not only minimizes significant interactions among the control loops, it permits the use of a very simple design criterion, namely the approximate assignment of the primary closed-loop poles to prespecified locations. A straightforward autotuning technique locates the closed-loop poles on-line so as to optimize the system set-point step responses. One desirable side-effect is to account for inexact decoupling. The controller is demonstrated using a simulated paper machine head box having an unusually large amount of (off-diagonal) interaction, a simulated two-input, two-output distillation column with time-varying parameters (varying gains and time delays), and a highly interacting unstable and non-minimum phase system on which the autotuning technique is demonstrated. These three processes place stringent requirements on any control method, and two of them have been used extensively in the literature to test various multivariable and/or self-tuning algorithms. Hence, the success of the new technique indicates that it is a very promising candidate to deal with intransigent processes, i.e. those characterized as unstable, non-minimum phase, time-varying (non-linear), and interacting.     

Adaptive fuzzy finite-time optimal control for switched nonlinear systems

This article addresses the adaptive fuzzy finite-time control problem for a class of switched nonlinear systems whose powers are positive odd rational numbers and vary with the switching signal. The fuzzy logic systems (FLSs) are used to approximate the unknown nonlinearities of the controlled systems, and then by combining backstepping control algorithm with adding a power integrator technique, an adaptive finite-time controller is designed. By modifying and optimizing the relevant design parameters of the proposed adaptive finite-time controller, a novel adaptive finite-time optimal control approach is developed. The proposed two adaptive finite-time optimal control schemes can guarantee semi-globally practically finite-time stability of the closed-loop system. Moreover, the adaptive finite-time optimal controller can also achieve optimized performance in relation to the cost functional. Finally, a simulation example is given to illustrate the effectiveness of the proposed two adaptive finite-time control strategies.     

Gain-scheduled controller design for linear parameter varying systems subject to pole assignment

This paper addresses a pole-assignment control problem for discrete-time linear parameter varying (LPV) systems. Based on LPV modeling approach, time-varying systems can be mathematically described via combining several linear systems and a specific weighting function. For the LPV systems, gain-scheduled (GS) control scheme is applied to deal with stabilization problem subject to pole-assignment constraint. Moreover, two cases of Lyapunov function are respectively employed to derive some sufficient conditions which belong to linear matrix inequality (LMI) problems. Solving those derived conditions, the corresponding GS scheduled controller can be designed such that the asymptotical stability and pole assignment of LPV systems are guaranteed. Finally, a controller problem of truck-trailer system is used to demonstrate the applicability and effectiveness of the proposed design methods.     

The effect of sample period on optimally designed servomechanism control systems

A uniform approach for comparing sampled-data servomechanism control systems with respect to the sample period is formulated such that a quadratic performance measure of the augmented continuous system states and discrete controller states is used both for controller design and performance evaluation. The structure of the controller and performance cost is optimally designed as a function of the sample period and converges to an optimal continuous control system as the sample period approaches zero. Extensive simulation reveals that the performance cost increases and that the norm of the controller gains decreases monotonically with the sample period.     

Adaptation Drift Suppression in Blood Glucose Self-Tuning Control

Abstract: To improve the glycemic regulation in clamping, a modification of the recursive least squares (RLS) estimation to be applied to any self-tuning adaptive control algorithm has been developed. It has been used in combination with a pole assignment controller, and its results have been compared through computer simulation in 12 test models with 3 other algorithms. It produces an improvement in the efficiency and the control cost, and it shows indications of ameliorating the stability. It also has been observed that for glycemic control, a minimum variance controller (control advance moving average controller [CAMAC]) is very efficient, whereas an empirical type of controller (Clemens) requires low control action. Some recommendations are made for the use of the algorithm in clamping in a hypothetical electromechanical endocrine artificial pancreas.     

Switching optimal adaptive trajectory tracking control of quantum systems

In this paper, a switching optimal adaptive controller for tracking a time‐dependent trajectory in finite‐dimensional closed quantum systems is proposed. The issue of intrinsic singularities in trajectory tracking control of quantum systems leads to a sharp rise in the control amplitude. To overcome this drawback, a switching optimal adaptive quantum controller is designed based on Lyapunov stability theory and optimal quantum control approach. A state‐dependent strategy is considered to select the switching signal. The new switching controller adjusts the quantum state so that its population traces the desired dynamic trajectory and simultaneously eliminates the effects of singularities and reduces the control amplitude. The proposed controller is tested successfully for population transfer in a 4‐level closed quantum system in a simulation experiment. Both issues of reduction of the tracking error and control intensity along with a significant decrease in the number of singular points are well illustrated by simulation experiment as the advantages of the proposed method.     

Inverse optimal control for asymptotic trajectory tracking of discrete‐time stochastic nonlinear systems in block controllable form

This paper concerns an inverse optimal control–based trajectory tracking of discrete‐time stochastic nonlinear systems. It is assumed that the nonlinear system can be transformed to the so called nonlinear block controllable form. Additionally, the synthesized control law minimizes a cost functional, which is posteriori determined. In contrast to the optimal control technique, this scheme avoids to solve the stochastic Hamilton‐Jacobi‐Bellman equation, which is not an easy task. Based on a discrete‐time stochastic control Lyapunov function, the proposed optimal controller is analyzed. The proposed approach is applied successfully to the two degrees‐of‐freedom helicopter with uncertainties in real time.     

Nonfragile reliable control for positive switched systems with actuator faults and saturation

This paper presents a nonfragile reliable control approach to positive switched systems with actuator faults and saturation. In order to guarantee the reliability of the controller, the controller gain matrix is chosen as the sum of a normal gain matrix and a gain perturbation matrix. A nonfragile reliable control is first proposed for the considered systems using a gain matrix decomposition technique. Then, the presented nonfragile control design approach is developed for the systems with exogenous disturbances. An approach to compute the normal gain matrix and the gain perturbation matrix is also provided. Under the obtained controller, the resulting closed‐loop systems are positive and L₁‐gain stable. Meanwhile, all the states will stay inside a cone. All presented conditions are described via linear programming. Finally, two examples are provided to verify the effectiveness of the theory findings.     

Stochastic control of networked control systems with packet dropout and time‐varying delay

This paper studies the stochastic stabilization problem for discrete‐time networked control systems with time delay and packet dropout. The message losses and time delay from the sensor to the controller and from the controller to the actuator are considered simultaneously. A two‐state Markov chain is used to model the correlated packet dropout process. By introducing free weighting matrices, the sufficient condition on the stochastic stability of such networked control system is obtained. An improved criterion is found by introducing the delay fractioning method and a new Lyapunov–Krasovskii functional. On the basis of the stability condition, the mode‐dependent controller is given in terms of linear matrix inequalities. A simulation example is given to show the proposed results. Copyright © 2012 John Wiley & Sons, Ltd.     

Structure and performance of discrete H∞ optimal control

In recent years a good deal of attention has been focused on the development of model-based controllers optimizing infinity-norm performance objectives. The motivation behind this is a perceived need for controllers which are more robust to modelling errors than those which result from conventional LQ designs. At the present time, however, numerical solution of the H∞ problems remains very much an open issue. This paper examines Grimble's approach to the design of discrete-time H∞ control laws for univariate plants subject to stationary stochastic disturbances. The structure of the controller is analysed using the internal model control concept of Garcia and Morari and is compared with that obtained for a polynomial LQ scheme. Simulation results are presented for both minimum phase and non-minimum phase systems in which the H∞ technique is seen to be inferior to LQ in terms of performance, robustness to parametric mismatch and computational complexity.     

Stochastic adaptive control of non-minimum phase systems

The explicit self-tuning control of linear systems with constant but unknown parameters is analysed. The class of single-input/single-output, discrete-time stochastic systems with coloured noise is considered without imposing a minimum-phase condition. A stochastic approximation type of identification algorithm coupled with a general linear control law structure satisfying weak conditions is shown to lead to the required stability properties of the closed-loop system. Similar approaches have been previously proposed for deterministic systems and for stochastic systems with uncorrelated disturbances. The specific example of a pole-shifting algorithm is considered and it is shown that the required asymptotic behaviour is achieved under certain conditions.     

Design of robust nonfragile H∞ controller for uncertain nonlinear polynomial systems

This paper is concerned with the robust H_∞ nonfragile controller design for a particular class of nonlinear systems, namely, the perturbed polynomial systems, which are subject to unstructured bounded uncertainties in both the system model and the control law. Combining the Lyapunov stability theory, properties of linear matrix inequality, and Kronecker product properties, a sufficient condition of robust H_∞ nonfragile control design is proposed. More specifically, we propose a robust H_∞ controller of nonlinear polynomial systems with additive unstructured uncertainties and variation in the control law itself that guarantee the stability and the attenuation of external perturbations. Two examples are provided to illustrate the effectiveness of the proposed approach.     

A decomposition approach to suboptimal control of discrete-time systems

A suboptimal controller for a class of discrete-time systems is presented. The controller is derived by first solving ‘off-line’ a simplified optimal control problem obtained by neglecting part of the system state and by considering a larger time step, then by solving ‘on-line’ at each time step an optimization problem based on the results of the previously solved ‘off-line’ problem. A simple numerical example is presented to illustrate the control scheme.     

POWELL'S METHOD APPLIED TO LEARNING NEURAL CONTROL OF THREE UNKNOWN DYNAMIC SYSTEMS

This paper describes a direct neural network (NN) learning controller that is capable of improving its performance in the control of a non-linear system whose dynamics are unknown. This controller is able to improve its performance without having to identify a model of the plant, which is a necessity for most existing neural network controllers. This characteristic is obtained with a gradient-free neural network learning algorithm, Powell's method. The performance of this new controller in the control of three non-linear systems, a pendulum, a double pendulum and a robot, was evaluated by simulations and experiments. The new controller has shown fast learning and small tracking error in the control of these systems.     

Optimal control of a class of pseudo Euler‐Lagrange systems

This paper presents a solution of the optimal control problem for a class of pseudo Euler‐Lagrange systems and proposes a systematic approach to find a Lyapunov function for stability analysis and controller synthesis for such systems. There are three main contributions of the paper. First, a systematic procedure is proposed and proved to construct a Lyapunov function for pseudo Euler‐Lagrange system directly from the mathematical structure of the differential equations, without the need to determine any kinetic or potential energy of the system first. Second, control methodologies for pseudo Euler‐Lagrange systems are also developed. In particular, an optimal controller is found for the case of second order dynamics yielding the same structure for the closed‐loop Lyapunov function as the one derived from the systematic procedure outlined as the first contribution. Finally, the optimal control methodology is extended to systems with order higher than two for a class of triangular systems. The method proposed here works for any mathematical model in the class of pseudo Euler‐Lagrange systems and is therefore not restricted to models of physical systems. Several examples illustrate the application of the novel approach, including mass‐spring‐damper systems and Van der Pol oscillators. Copyright © 2016 John Wiley & Sons, Ltd.     

Guaranteed-cost stabilization of non-linear stochastic systems

The control of uncertain non-linear discrete-time systems having stochastic cone-bounded non-linearities is considered. First, a quadratic performance bound and a guaranteed-cost optimal state feedback controller are derived. Then, an auxiliary system is introduced. It is shown that the quadratic optimal control for this auxiliary system is the same as the guaranteed-cost control for the original system, and, therefore, the existence of the infinite-horizon guaranteed-cost controller can be based on the stabilizability and observability properties of the auxiliary system. Finally, the stochastic boundedness of the controlled uncertain system is proved based on the properties of the auxiliary system. © 1998 John Wiley & Sons, Ltd.     

Neural net control of nonlinear plants through state feedback

A heuristic design method for state feedback fixed (non‐adaptive) neural net controller in nonlinear plants is presented. The design method evolves as a natural extension of the optimal control strategies employed in linear systems. A multi‐layered feed‐forward neural network is used as the feedback controller. The controller is trained to directly minimize a suitable cost function comprised of the plant output, states and the input. The optimization is carried out using a gradient scheme that employs the recently developed concept of block partial derivatives. The applicability of the proposed design method is demonstrated through simulated examples. Simulation studies include a variety of optimal control problems in nonlinear plants such as: minimum energy and minimum fuel problems, state tracking, output servo with integrator, and unconstrained and constrained regulation. Copyright © 2000 John Wiley & Sons, Ltd.