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This paper investigates the linear quadratic regulator (LQR) problem for continuous-time linear systems with redundant control inputs. The LQR control problem has been widely studied, but due to technical difficulties, there is little advance in the study of adding input redundancies. To address this problem, a convergent matrix series, the limit of a monotonically decreasing sequence, is first presented as an upper bound of the symmetric positive definite solution of a class of continuous algebraic Riccati equations (CAREs). Compared with the existing studies on this topic, the obtained bounds are more precise. Moreover, by utilising these upper bounds in the LQR problem of adding input redundancies, a class of sufficient conditions is presented to decrease the quadratic performance index. Finally, the corresponding numerical examples are given to illustrate the effectiveness of our results and compare them with the existing results. Meanwhile, some simulation experiments show that systems with redundant control inputs have good control performance. [ABSTRACT FROM AUTHOR]

The problem of $ L_1 $ L 1 output tracking control of positive linear systems in finite time is addressed in this paper. By constructing a linear copositive Lyapunov–Krasovskii functional, some sufficient conditions are achieved to ensure that the states are finite-time bounded and the measurement outputs have $ L_1- $ L 1 − gain performance for given systems, respectively. Next, a state feedback controller is designed to ensure that the output signals of the tracking system can effectively trace the specified signals of reference model with finite-time boundedness and $ L_1 $ L 1 -gain performance. Finally, an example is given to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper intends to analyse the disturbance rejection and output tracking control for a class of nonlinear control systems with disturbances. In this connection, we present a method that combines a proportional-integral observer and nonlinear-equivalent-input-disturbance estimator for superior disturbance rejection performance. Specifically, the nonlinear-equivalent-input-disturbance estimator comprises of equivalent-input-disturbance estimator and nonlinear feedback term, which is employed to estimate and reject the disturbances from the nonlinear system. Notably, the proportional-integral loop in the proportional-integral observer reduces the estimation inaccuracy of the nonlinear-equivalent-input-disturbance. Then the estimated disturbance is intertwined into the repetitive control input to compensate it efficiently. In order to obtain the required results, the proposed control system is converted into a two-dimensional modified repetitive control system to describe the learning and control actions. In particular, the proposed controller enables to adjust the gains directly to improve the learning and control performance and as a result, the tracking accuracy increases. Using a general Lyapunov–Krasovskii functional, singular value decomposition technique and linear matrix inequalities approach, a design algorithm for establishing proportional-integral observer and feedback gains is developed for the system under consideration. Finally, simulation results are given to illustrate the developed method's validity and superiority. [ABSTRACT FROM AUTHOR]

This paper investigates the aperiodic sampling stabilisation problem for a class of switched linear systems under asynchronous switching. Based on a novel dynamic sampling rule, a sampling-point-based partition-dependent discontinuous Lyapunov functions control approach are developed to make the considered closed-loop switched systems be globally asymptotically stable. Compared with the existing results, the proposed control method permits frequent switching in a sampling interval for subsystems. But the frequent information transmission to the matched controllers and the negative effect of long asynchronous running on system performance can be nicely handled in this paper. Moreover, the partitioned Lyapunov functions are allowed to increase in some segments of the synchronous operating intervals. Tighter synchronous duration and switching number which are determined by more than affine functions make the switching signal more flexible. Finally, simulation analyses of two examples show the advantages of the developed control strategy. [ABSTRACT FROM AUTHOR]

This paper considers a constrained co-design problem for linear time-invariant (LTI) systems. With a practical vision of real-world problems, constraints on the control signal and system states are involved in the proposed algorithm. The main goal is to design a sub-optimal controller by simultaneously obtaining the control policy and the model parameters. To this end, the conventional problem of solving the Hamiltonian-Jacobi-Bellman (HJB) equation is transformed into a nonlinear non-convex optimisation problem. Then, by reformulating the constraints of the optimisation problem, it is relaxed into a convex Semi-Definite Programming (SDP). By presenting an iterative method, the control cost, the performance, and the number of iterations are improved compared to conventional methods, and a closer result to the optimal solution is obtained. The performance and efficacy of the proposed algorithm are investigated through a case study on the physical load positioning system. [ABSTRACT FROM AUTHOR]

This paper discusses the output-feedback-based model-free optimal output tracking control problem of discrete-time systems with completely unknown system models under mild assumptions. The only information that allows utilisation is the system output and the reference output. To overcome these challenges, the paper aims to solve a model-free optimal output regulation problem for achieving optimal output tracking control; solving an optimal output regulation problem is equivalent to solving a linear quadratic regulation (LQR) problem and a constrained static optimisation problem. The state reconstruction is first given to represent the system state in terms of the input and output sequences. A data-driven value iteration (VI) algorithm is then proposed to iteratively approximate the solution to the discrete-time algebraic Riccati equation (ARE) of the corresponding LQR problem on the basis of input and output data. Next, based on the iterative solutions with respect to the ARE, a model-free solution is provided for the corresponding constrained static optimisation problem. Finally, an alternative reference system equivalent to the original reference system is established to avoid the requirement of having the knowledge of the reference system dynamics and the reference state. A numerical example is employed to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper presents a novel prespecified finite-time and overshoot-restrained fault-tolerant tracking control scheme to compensate the intermittent faults in linear uncertain systems. Starting from the system tracking error dynamics model, we design a speed excitation function to improve the response speed of the control. A finite-time performance index function is established in the zero-sum game framework for the fault-free H ∞ optimal control policy. Based on Lyapunov stability theory, a fault compensation oriented fault estimation and diagnosis method is proposed to ensure the uniformly ultimately bounded stability of tracking errors. It is noteworthy that the proposed speeding fault-tolerant control can accelerate the trajectory tracking, narrow the upper bound of tracking errors and restrain the overshoot. Numerical and practical experiments fully illustrate the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

Control of time-varying systems has become increasingly popular in recent years, as various domains such as aviation, automobile and manufacturing industries require a quick and precise response in the presence of uncertainties. Adaptive control, a popular strategy is used to control systems with unknown or time-varying properties. Classic adaptive control is insufficient to cope with time-varying parameters to produce desired results with minimal parametric error. Furthermore, for these strategies to work, identification model must be initialised closer to the plant. Else the transient response of the plant is likely to grow unbounded. This paper mainly concentrates on employing adaptive control for a type of linear time-invariant (LTI) and linear time-varying (LTV) systems. The time variations in LTV plant parameters are either slow, rapid or fast. This research in turn proposes a two-stage adaptive scheme which swiftly determines the compact region in which plant parameters reside. This method in turn ensures atleast one model to be initialised closer to the plant which significantly reduces parametric estimation error. The uniform boundedness of identification error, tracking error as well as the parametric error of LTI and LTV systems, are deduced. Sufficient examples are also considered to demonstrate the efficacy of the proposed two-stage scheme. [ABSTRACT FROM AUTHOR]

This paper concerns to an event-triggered control for switching linear systems. For reducing the data transmission amount of the communication network from sensor to controller, a switching-mode independent dynamic event-trigger (DET) is constructed wherein a positive constant and a positive auxiliary variable are simultaneously involved. Based on the received discrete-time state measurements, a mode-dependent feedback control law is proposed. Given some prior activation probabilities of switching signal, an average dwell time (ADT) based controller designed method is presented. It is proved that the closed-loop system achieves Zeno-free mean square bounded exponentially stable (MSBES). Significantly, the minimal event-triggered interval can be accurately given while the maximal event-triggered interval can be approximated. Numerical examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the optimal tracking problem for discrete-time linear systems with multiple delays is studied without system dynamics. It is known that the total state of a system without specific dynamic characteristics is hard to be measured, unless such a system is equipped with massive sensors, which, however, may lead to an increase in cost and complexity for analysing. To deal with this problem and avoid adverse effects caused by using system state information, a new data-driven value iteration (DDVI) algorithm is proposed by considering three factors: past control inputs, system outputs, and external reference trajectories. Before the algorithm is proposed, a transformation is made to the original system according to the characteristics of the time-delay system, so that the time-delay number can be reduced or become a delay-free system. A novel data-driven state equation is derived from the historical data of the three factors, and then, it is adopted to solve the optimal control of multi-delay systems. Further results show that the proposed DDVI algorithm is convergent and the tracking error is asymptotically stable. Finally, simulations are provided to show the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

This paper presents a systematic method to design a high-order repetitive model reference controller (HO-RMRC) for a discrete-time linear system that is subject to uncertain periodic references and disturbances. The controller design method we propose is established by combining two controller design schemes: high-order repetitive control (HORC) and model reference control (MRC). Here, the HORC is used to suppress uncertain periodic disturbances significantly and the MRC is used to track time-varying references without introducing new transient responses. The stability analysis of the resulting closed-loop system is provided and describes how admissible learning gains are determined to achieve stability and a desirable convergence rate. The efficacy of the proposed control method is demonstrated via numerical simulations where the performance of the resulting HO-RMRC is compared with those of the HORC and the MRC as standalone controllers. It is evident that the HO-RMRC outperforms the HORC and the MRC in simultaneously achieving perfect reference tracking and disturbance cancellation/attenuation. [ABSTRACT FROM AUTHOR]

This paper talks about asymptotic convergence aspects about the internal model principle (IMP) and trajectory tracking control (TTC) in linear dynamical systems. First, IMP and asymptotic TTC are re-formulated and explicated. Second, TTC under internal models of trajectory and disturbance is classified in terms of tracking error bias into bounded; nonzero steady-state; zero steady-state; unbounded (tracking failure). Third, TTC attainability and tracking error biases are examined via asymptotic convergence analysis. In particular, bounded TTC is attainable if trajectory and disturbance are essentially bounded; zero/nonzero-steady-state TTC is attainable if trajectory and disturbance t → ∞ limits are well-defined so that the Laplace ultimate value theorem holds; zero-steady-state TTC is realisable if internal models exactly reflect all unstable modes of trajectory and disturbance. Fourth, when internal models are subject to mismatches and sampled-data approximates, several interesting convergence facts are revealed. More specifically, for addressing zero-steady-state TTC to periodic trajectory and disturbance, stabilisation may be insufficient; for addressing TTC under sampled-data internal models, unknown convergence features are claimed. Finally, TTC controller parametrisation via pole assignment stabilisation is scrutinised under static output and state feedback. Numerical examples are included to illustrate the main results. [ABSTRACT FROM AUTHOR]

This paper studies the robust static output feedback control of discrete-time Markov jump systems considering that the mode of operation cannot be directly measured. It is assumed that the only available information concerning the main jump process comes from a detector, so that the jump and detector processes can be modelled as a hidden Markov model. Initially, it is considered that the system's dynamic matrix is subject to parametric uncertainties. By assuming a full row rank condition for the output matrix and employing a clusterisation technique for the state space of the hidden Markov model, it is derived a set of linear matrix inequalities (LMIs) that guarantees robust stability in the mean-square sense of the closed-loop system, as well as a bound on its H 2 norm. It is also shown that this design technique is linked to the bounded real lemma, so that a new set of LMIs conditions can be obtained for the 'pure' H ∞ control problem, which can be extended to cover the robust polytopic case. The paper is concluded with an illustrative example. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the semi-global asymptotic stabilisation of fractional-order (FO) linear systems subject to actuator saturation by output feedback. To solve the problem, a family of observer-based linear output feedback laws, parameterised in a positive scalar, is proposed by means of the low gain feedback design technique. The design applies to FO linear systems that are stabilisable and detectable, but not exponentially unstable. For such an FO system under the proposed observer-based linear low gain output feedback, the peak value of the control input for a given initial condition can be made arbitrarily small to avoid actuator saturation by decreasing the value of the parameter towards zero and thus semi-global asymptotic stabilisation is achieved. To obtain these results, we establish the properties of low gain feedback, derive asymptotic expansions and the bounds of high-order derivatives of the Mittag-Leffler (ML) functions to estimate the state responses of FO linear systems, and explicitly construct a Hermitian matrix to satisfy a linear matrix inequality (LMI) stability condition for FO linear systems. The results in this paper extend the corresponding results for integer-order (IO) linear systems. [ABSTRACT FROM AUTHOR]

In this paper, an event-triggered P-type iterative learning control (ILC) scheme is developed, where the control input update only occurs in the event-triggered iterations. The event-triggered iterations are determined by a pre-defined event-triggering condition, which is composed of two parts, one is the threshold condition to ensure convergence, the other is derived from the Lyapunov stability principle to ensure stability. The convergence analysis theorem is deduced mathematically. Further, using similar steps, event-triggered PD-type ILC and event-triggered PID-type ILC are proposed. Finally, the simulation results illustrate that the presented algorithms can ensure that the error converges and make the control input update less frequently, so as to realise the goal of saving resources. [ABSTRACT FROM AUTHOR]

In this paper, a gain determining method for nonlinear adaptive backstepping technique is proposed by the pole placement method. By introducing a subsystem that can be linearised as a linear system, controller gains can be solved by the pole placement method. Compared with the existing techniques, the proposed method can achieve a transient performance like a linear system with the pole placement method instead of constraining the system in a predefined performance range. Meanwhile, the proposed method does not change the structure of adaptive backstepping controllers, which preserves the advantages of the original backstepping design and avoids increasing the computing effort for the control system. In addition, the applications of the proposed method are demonstrated by three examples, including a 2nd-order nonlinear system, a 3rd-order nonlinear system, and a single-link robot arm. The corresponding simulations are conducted, and the simulation results are illustrated and analysed. Moreover, comparative simulations are conducted to verify the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with the stabilisation problem of linear systems subject to saturated input and bounded disturbance via event-triggered control strategy. In a hybrid systems framework, both a state feedback law and a static output feedback law are proposed to design the event-triggered controllers, which provide solutions to the event-triggered control collaborative design problem. For the case of using static output feedback, an iterative linear matrix inequality algorithm is proposed to obtain the feedback gain. In addition, the local uniform ultimate boundedness of the closed-loop system is ensured. Finally, two examples are given to illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

In this paper, high-order fully actuated (HOFA) models with multiple orders for general dynamical control systems are firstly proposed, for which controllers can be easily designed such that the closed-loop systems are constant linear ones with completely assignable eigenstructures. Based on this special feature of the type of HOFA models, controllability of general dynamical control systems is proposed. It is revealed that a general dynamical control system can be represented by a controllable subsystem described by a HOFA model, and an extra uncontrollable one or supplementary one. While a general dynamical control system is called stabilisable if its uncontrollable (autonomous) subsystem does not exist, or is stable in a certain sense. Finally, two parametric design approaches for control of the type of general HOFA models are proposed, which provide all the design degrees of freedom. Several examples, including ones of sub-fully actuated systems, are treated, which demonstrate the effect of the proposed theories. [ABSTRACT FROM AUTHOR]

This paper deals with the state feedback control for linear systems in the presence of state delay using a direct numerical design methodology. The design algorithm iteratively searches the solution space of controller parameters to find a proper controller gain that guarantees the delay-independent stability of the closed-loop system. The algorithm divides the solution space to some simplexes, selects one simplex and evaluates two checking methods on this simplex. The first method checks the stabilisability of the corner points (to establish the feasible point) and the other detects the total infeasibility (total de-stabilisability) of the simplex (to omit the undesired parts). One interesting property of the method is its capability in detecting total de-stabilisability of a simplex through its corner points. If none of these methods is successful, the simplex is divided into two smaller ones which will be checked in the next algorithm's iterations. According to the direct search nature, the algorithm is non-conservative and assuredly reaches a stabilizable point in the feasible space of the design space. The proposed algorithm and previous methods are evaluated on a set of random generated systems to compare the feasibility of the methods. Simulation results reveal the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper studies the h-stabilisation problem of certain classes of perturbed systems on time scales. Sufficient conditions for the control law design are proposed to ensure the h-stability of the closed-loop dynamical system under Lipschitz-type disturbances. Using the Gronwall inequality approach with time scale theory, the h-stability of the closed-loop system is investigated in non-uniform time domains with bounded graininess. Some numerical examples are provided to show the feasibility of the obtained results using the proposed approach for systems evolving on some arbitrary time scales. [ABSTRACT FROM AUTHOR]

This paper is devoted to study the issue of event-triggered observer-based H ∞ control of switched linear systems subject to time-varying state delay and exogenous disturbance. Firstly, an observer-based event-triggered controller is provided under the proposed event-triggered mechanism. Then, based on the average dwell time scheme and Jensen's Inequality technique, delay-dependent less conservative sufficient conditions in terms of Linear Matrix Inequalities (LMIs) are obtained to guarantee the resulting augmented switched systems is exponential stabilisation and satisfies a prescribed H ∞ control performance. Furthermore, observer-based event-triggered controller is designed, and it is shown that there exists a positive lower bound of inter-event intervals. Finally, numerical example and comparison results are provided to illustrate the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

We show that every forward-flat nonlinear discrete-time system with two inputs can be transformed into a structurally flat normal form by state- and input transformations. This normal form has a triangular structure and allows to read off the flat output, as well as a systematic construction of the parameterisation of all system variables by the flat output and its forward-shifts. For flat continuous-time systems, no comparable normal form exists. [ABSTRACT FROM AUTHOR]

In this paper, the problem of finite-time observer-based control for linear fractional-order systems with interval time-varying delay is studied. The delay is assumed to vary within an interval with known lower and upper bounds. A new proposition on estimating Caputo derivatives of quadratic functions is given. Based on the proposed result, delay-dependent sufficient conditions for finite-time stability and for designing state feedback controllers and observer gains for observer-based control problem are established in terms of a tractable linear matrix inequality and Mittag–Leffler function. A numerical example with simulation is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of Static Output Feedback (SOF) stabilisation for continuous-time linear systems subject to norm-bounded parameter uncertainties using the Linear Matrix Inequality (LMI) approach. Usually, this issue leads to the feasibility of a Bilinear Matrix Inequality (BMI), which is difficult to linearise to get non-conservative LMI conditions. We present first, in this paper, some background results on the SOF controller design and that are found to be extended to the case of norm-bounded uncertainties. We show that some restrictions on the feasibility of these results should be guaranteed. Moreover, by means of some technical Lemmas, we transform the BMI into a new LMI with a line search over a scalar variable. An enhanced and less conservative LMI condition with a line search over two scalar variables is also developed. Furthermore, a simplified version of each LMI condition without a priori fixed parameters is also presented. An extensive portfolio of numerical examples is presented in order to evaluate the conservativeness and to show the superiority of the proposed design method to the background results. [ABSTRACT FROM AUTHOR]

A numerical method is proposed to reduce the complexity and computational effort involved in the application of the multiparametric linear programming technique in the design of offline controllers for linear systems subject to constraints. For this purpose, the concept of controlled invariant sets and the K q-flat data cluster analysis algorithm are applied. Specifically, we show how the K q-flat algorithm can be used to establish a smaller number of polyhedral regions associated with a piecewise affine explicit state feedback control law. We also propose a new approach in the design of sub-optimal controllers that further reduce the number of regions. Numerical examples show that a significant reduction in the complexity of the control law can be achieved by the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers the stochastic optimal control of a multi-period mean-variance trade-off performance criterion with and without constraints for discrete-time linear systems subject to multiplicative noises. We adopt a mean-field approach to tackle the problem and obtain a solution for the unconstrained case in terms of a Riccati-like difference equation. From this general result, we obtain a sufficient condition for a closed-form solution for one of the constrained problems considered in the paper. When particularised to the portfolio selection problem, we show that our results retrieve some of the results available in the literature. We conclude the paper by illustrating the obtained optimal controls with a multi-period portfolio selection problem where we minimise the sum of the mean-variance trade-off costs of a portfolio against a benchmark along the time. [ABSTRACT FROM AUTHOR]

In this paper, the model-based event-triggered control is addressed for a class of linear systems with two time scales. The singular perturbation technique is used to analyse the stability of the event-triggered control closed-loop system with a dual-stage event-triggering condition. For the differences between the matrices of the plant and the model, the relations between the parameters in the event-triggering conditions are revealed for the stability and the sampling performance of the closed-loop systems. Specifically, the parameters in the event-triggering conditions can be selected in a range independent of the matrices in the model. Finally, two numerical simulations are provided to illustrate the efficiency and feasibility of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the H ∞ static output feedback control problem for linear systems. The sensor and actuator may simultaneously suffer the total/partial loss of effectiveness. An adaptive fault-tolerant control scheme is developed by combination of linear matrix inequality method and adaptive mechanism. By estimating the inverses of failure factors online, the adverse effects of sensor and actuator failure can be compensated for. Finally, simulation results on the 'Raptor-90' helicopter verify the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a new problem of static output feedback controllers design for positive systems with delayed output measurements. When delayed output measurements are exclusively used as feedback control signals, previous control design methods for positive systems relying on the so-called delay-independent positivity and stability conditions are unable to synthesise a stable static output feedback controller for positive systems. A new method based on delay-dependent positivity and stability conditions is proposed in this paper to tackle this issue. We show that the synthesis of static output feedback controllers for positive systems under the effect of delayed output measurements is feasible under the newly proposed design method. Numerical examples are given to demonstrate the effectiveness of the new result. [ABSTRACT FROM AUTHOR]

The existing off-line observer/controller identification (OCID) method for linear systems is newly extended in this paper for off-line/on-line identification of known/unknown highly nonlinear systems, and a new input-constrained active fault-tolerant tracker is developed, based on the identified linear models. The advantages of the proposed extended on-line OCID method for linear/nonlinear systems are briefly described as follows: (i) Implement novel servo-control-oriented off-line OCID methods in observer and controller canonical forms for highly nonlinear systems; (ii) Is able to overcome the discontinuity induced by the singular value decomposition (SVD) that should be carried out at each sampling instant; (iii) It directly realises the identified parameters in the observer/controller canonical forms; this simplifies the identification process; (iv) Can be practically implemented for the on-line control of an unknown nonlinear system which was constituted by an unknown open-loop plant, an existing but unknown controller and/or an unknown observer; and (v) Can be utilised to develop a new active fault-tolerant controller to compensate the immovable existing controller of the practical operating system. Finally, the servo-control-oriented off-line OCID method for the highly nonlinear PUMA 560 manipulator is shown in the illustrative examples to demonstrate the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the preview control problem for a class of linear continuous time stochastic systems with multiplicative noise is studied based on the augmented error system method. First, a deterministic assistant system is introduced, and the original system is translated to the assistant system. Then, the integrator is employed to ensure the output of the closed-loop system tracking the reference signal accurately. Second, the augmented error system, which includes integrator vector, control vector and reference signal, is constructed based on the system after translation. As a result, the tracking problem is transformed into the optimal control problem of the augmented error system, and the optimal control input is obtained by the dynamic programming method. This control input is regarded as the preview controller of the original system. For a linear stochastic system with multiplicative noise, the difficulty being unable to construct an augmented error system by the derivation method is solved in this paper. And, the existence and uniqueness solution of the Riccati equation corresponding to the stochastic augmented error system is discussed. The numerical simulations show that the preview controller designed in this paper is very effective. [ABSTRACT FROM AUTHOR]

In the fault-tolerant control theory based on model following control, the desired signal of the control system is the output of a reference system. This paper is concerned with the design of the preview controller for a class of fault systems. A composite vector is introduced by including error vector, fault system state vector and reference system state vector. Then, we derived an augmented system from the known system equation, in which the reference input has equal status with the desired signal in the traditional preview control theory. Therefore, we can use the known theory to design the preview controller for the augmented system, then the preview controller of the original fault system can be obtained by the integration method. This paper strictly discusses the connection between stabilisation and detectability of the augmented system and the corresponding characteristics of the original system. Finally, by applying this theory to a real steam generator water level control system, it is found that the actions of the reference input preview and the fault signal preview can effectively eliminate the effect of the fault signal on the water level of the steam generator. The simulation shows the effectiveness of the controller designed. [ABSTRACT FROM AUTHOR]

The optimal control of linear quadratic model is given in a feedback form and determined by the solution of a Riccati equation. However, the control-related Riccati equation usually cannot be solved analytically such that the form of optimal control will become more complex. In this paper, we consider a piecewise parametric optimal control problem of uncertain linear quadratic model for simplifying the form of optimal control. By introducing a piecewise control parameter, a piecewise parametric optimal control model is established. Then we present a parametric optimisation method for solving the optimal piecewise control parameter. Finally, an uncertain inventory-promotion optimal control problem is discussed and a comparison is made to show the effectiveness of proposed piecewise parametric optimal control model. [ABSTRACT FROM AUTHOR]

A two-steps method of designing switched linear systems is presented with the parameterization of globally uniformly asymptotically stabilising controllers with average dwell time (ADT). First, an observer-based switching controller design is given for a class of switched linear system. Based on the construction of observer-based controller, conceptions of doubly coprime factorization and Youla parameterization of LTI systems are extended to switched linear systems with respect to globally uniformly asymptotical stability (GUAS) using a state-space expression. Second, the parameterization of closed-loop systems, which are affine with any globally uniformly asymptotically stable -parameter, is then described. This description enables the application of the -- parameter approach to a variety of switched linear control-system designs. The control construction provides us a two-steps process design procedure. Above all, based on the Schur complementary lemma and controller variable elimination method, a systematic weighted L2 performance strategy is focused on and a design scheme of to obtain weighted L2-gain performance is clarified. Finally, a numerical example is given to show the validity and potential of the developed results. [ABSTRACT FROM AUTHOR]

The control objective for wind turbine control systems includes maximum power tracking, speed and power regulation and minimisation of mechanical loads. The operating region of a wind turbine is a function of the incoming wind speed and the control objective in each operating region differ significantly from the other. Therefore, a linear controller designed based on a model obtained at one operating point cannot guarantee stability and satisfactory performance across the whole operating regime of the turbine. In this paper, a continuous-time multi-model predictive controller is proposed for variable-speed variable-pitch wind turbine systems. Four controllers were designed using linearised models obtained at 4, 8, 11 and . A Bayesian probability inference function was used to make the transition between these controllers based on the errors between the system outputs and each operating point. Simulation studies based on a benchmark 5 MW wind turbine were used to demonstrate the performance of the proposed controller. [ABSTRACT FROM AUTHOR]

In this study, we present an extension of the prediction scheme (dynamic control) for nonlinear stochastic systems with both input and state delays. The stochastic system includes multiplicative noise and it is modelled as Ito stochastic differential equation. Input delay is considered to be equal or less than state delay and both delays are considered to be constant. At first, a new formula for prediction of the system's state is presented and then by means of this prediction vector, control input is constructed. To calculate the stabilising gain of the predictive controller, some sufficient delay-independent conditions in the form of linear matrix inequality are presented. Finally, simulation examples are given to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an approximate model and propose a piecewise optimisation method to simplify the expression of optimal control for an uncertain linear quadratic optimal control problem. First, we consider an optimal control problem of uncertain linear quadratic model under optimistic value criterion. Based on the equation of optimality, we deduce an analytic expression of optimal control. Then, we study an approximate model with control parameter and propose a piecewise optimisation method for solving the optimal parameter of such an approximate model. As an application, a four-wheel steering vehicle optimal control problem is given to show the utility of the proposed approximate model and the efficiency of the proposed piecewise optimisation method. [ABSTRACT FROM AUTHOR]

The paper is concerned with the control of a linear plant with an output delay. As is known, when the plant parameters do not vary in time, the transfer function approach can be used to find a high-performing controller with the Smith-predictor structure. Such an approach in the domain of the Laplace transform is not directly applicable in the time-variant case. Nevertheless, it is shown that the transfer function of the Smith controller valid for constant values of the parameters can be realised in such a way that closed-loop stability, as well as point-wise optimal performance, is ensured also when the parameters vary with time. The suggested technique is applied to the control of a heat exchanger whose varying parameters include a measurement delay. [ABSTRACT FROM AUTHOR]

This paper describes the combination design of predictive functional control (PFC) and optimal linear quadratic (LQ) method for a kind of nonlinear process with output feedback coupling. In many existing control methods for this kind of nonlinear systems, the nonlinear part is either ignored or represented as a rough linear one when corresponding predictive control methods are designed. However, by assuming that the nonlinearity can be ignored or simplified to a linear time-varying part may not lead to the good control performance of subsequent linear control designs. The paper is a further investigation on this kind of systems, in which a procedure of PFC plus a modified optimal LQ control is developed. With respect to the proposed control strategy and the corresponding processes, the closed-loop performance is improved concerning tracking ability and disturbance rejection compared with previous predictive control methods. In addition, the proposed control is easy to implement as it selects a simple structure and a modification of the classical control scheme. [ABSTRACT FROM PUBLISHER]

In this paper, a class ofh-difference linear control systems with two fractional orders is studied. We use the Caputo typeh-difference operator. The formula of the solution to the stated initial value problem of the given system is proved. The problem of controllability in a finite number of steps is studied. [ABSTRACT FROM PUBLISHER]

In this paper, we deal with the problem of stochastic Nash differential games of Markov jump linear systems governed by Itô-type equation. Combining the stochastic stabilizability with the stochastic systems, a necessary and sufficient condition for the existence of the Nash strategy is presented by means of a set of cross-coupled stochastic algebraic Riccati equations. Moreover, the stochasticH2/H∞control for stochastic Markov jump linear systems is discussed as an immediate application and an illustrative example is presented. [ABSTRACT FROM AUTHOR]

This article investigates a new adaptive non-linear compensation controller for a class of time-delay non-linear systems with partly known dynamics. First, a non-linear neural-network(NN)-based identification model that includes a prior knowledge about the plant dynamics is discussed by using the approximation capabilities of NNs. Then, the adaptive non-linear compensation controller is developed to produce the desired tracking performance. The proposed controller based on the NN can reduce the effect of modelling uncertainties and provide the time-delay compensation, while stability of the closed-loop system is guaranteed. The effectiveness of the proposed scheme is demonstrated through the application to the control of a continuous stirred tank reactor. [ABSTRACT FROM AUTHOR]

Some fundamental properties of observability and controllability are studied for linear discrete-time systems in a bandwidth-limited communication network environment shared by a number of sensors and actuators and a remote controller. The concepts of finite time set-observability and set-controllability are introduced for such systems. Sufficient and necessary conditions on quantisation level for set-observability and set-controllability are derived. Especially, the admissible data rates of the communication network are obtained that are sufficient and necessary for the system to be finite time set-observable or finite time set-controllable. In addition, less conservative sufficient and necessary rates based on quantisation level of system states are given too. [ABSTRACT FROM AUTHOR]

This article deals with the robust H2 control problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration appear both in the system parameters and in the mode transition rates. First, a new criterion based on linear matrix inequalities is established for checking the robust H2 performance of the uncertain system. Then, a sufficient condition for the existence of the state-feedback controllers is established such that the closed-loop system is quadratically mean square stable and has a certain level of robust H2 performance in terms of linear matrix inequalities with equality constraints. A globally convergent algorithm is also presented to construct such controllers effectively. Finally, an illustrative numerical example is used to demonstrate the developed theory. [ABSTRACT FROM AUTHOR]

This article considers the delay-dependent H∞ control problem for linear neutral systems with both discrete and distributed delays. The problem we address is to design a state feedback controller such that the resulting closed-loop system is asymptotically stable and satisfies a prescribed H∞ performance level. First, a delay-dependent sufficient condition for the solvability of the problem is obtained in terms of matrix inequalities. Then, by using the cone complementarity linearization approach, an H∞ controller is developed based on the solvability condition. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Using the innovation analysis method in the time domain, based on the autoregressive moving average (ARMA) innovation model and white noise estimators, a pole-assignment fixed-interval steady-state Kalman smoother is presented for discrete-time linear stochastic systems. It avoids the computation of the optimal initial smoothing estimate, and can rapidly eliminate the effect of arbitrary initial smoothing estimate by assigning the poles of the smoother, with an exponentially decaying rate. Several simulation examples show its effectiveness. [ABSTRACT FROM AUTHOR]

The topic of this study is output feedback control of linear control system with output. Use of condensed forms of the linear system under static output feedback (SOF) control is made to derive sufficient conditions for stabilization. A minimal-order control-free observer is presented. [ABSTRACT FROM AUTHOR]

This note studies the existence of solutions to MIMO linear systems under decentralized relay feedback containing hysterisis. A necessary and sufficient condition is presented to guarantee the extended solutions at the so-called intersecting instant. The suggested method is to examine the sign of the first non-zero derivative of each output right after the switches occur. Illustrative examples are given to show the cases of non-existence and non-uniqueness of solutions. [ABSTRACT FROM AUTHOR]

Fractional Order Control methods were applied to a three-axis reaction wheels satellite altitude control system. To show the advantages of this method, a comparative study between a Linear Quadratic Regulator and a Fractional Order Control was established through two principal fractional control laws. The aim is to establish an efficient control law which satisfies a given specification and maintains sufficient stability and accuracy even under the strong effects of intrinsic parameters uncertainties, and also external perturbations. [ABSTRACT FROM AUTHOR]

A unified framework to the initial condition response (ICR) analysis of non-linear time-varying systems of the Lur'e type and linear time-invariant (LT]) systems is considered. To quantify the transient behaviour resulting from initial conditions, an ICR measure is defined. An appropriate upper bound for the ICR measure can be calculated based upon the condition number of a positive definite matrix, associated with a quadratic Lyapunov function. Owing to the particular structure of the Lur'e systems, bounding the ICR measure is transformed into a minimization problem, constrained by either two simultaneous Lyapunov matrix inequalities or a single algebraic Riccati inequality. In the LTl case, the ICR measure is merely the supremum of the induced norm of the state transition matrix and its calculation involves solving a Lyapunov matrix equation. The ICR measure bound is significant from the engineering standpoint since it enables the calculation of the non-saturating domain of the state variables. In the LTI case, this bound also provides a quantification of impulse and unit step responses. The results are illustrated by several examples. [ABSTRACT FROM AUTHOR]