Class Of Continuous-time Linear Systems Research Articles

Nash Equilibrium-Based $$ H_\infty $$ Optimal PI Preview Control for a Class of Continuous-Time Linear Systems

Nash Equilibrium-Based $$ H_\infty $$ Optimal PI Preview Control for a Class of Continuous-Time Linear Systems

Output feedback sliding mode control based on non-singular terminal sliding mode observer

In this article, the finite-time output feedback sliding mode control problem is investigated for a class of continuous-time linear systems with unmeasurable states. First, a novel terminal sliding mode observer is established to estimate the unmeasured system states. Second, a novel integral sliding surface is introduced with tunable parameters. Then, an output feedback sliding mode controller with power terms is constructed to drive the given system to the origin in a finite time. A switching from the terminal sliding mode to a usual sliding manifold is taken to avoid singularity problem. Finally, two application-oriented examples are offered to verify the effectiveness of the proposed algorithm.

New Approach to Fast and Hyperstable State Observers for Stochastic and Complex Systems

This paper is concerned with the fast state observer for a class of continuous-time linear systems with unknown bounded parameters and sufficiently slowly time varying which satisfy the usual assumptions of conventional state observer for time-invariant plants. A less conservative approach based on hyperstability analysis is proposed to deal with the tracking error involved in Popov’s inequality. Sufficient conditions that ensure the asymptotic stability of the closed-loop system are established and formulated in term of a nonlinear part which is designed with appropriate proportional and derivative gains. This observer included the derivative of the estimation error. The results obtained are satisfactory and less conservative than the Lyapunov stability analysis for the estimation error dynamic system. Also, it is showed that with a good choice of Proportional-Derivative (PD) gains, it is possible to reduce in this case to zero, the estimation error on the one hand, and on the other hand to reduce it to small residues in an asymptotic way. Finally, a numerical example of a lateral motion of CESSNA 182 aircraft system is presented to reconstruct the sideslip angle and the roll angle, respectively, and to highlight the efficiency of the approach that has been developed.

Event-based state estimation under constrained bit rate: An encoding–decoding approach

This paper is concerned with the state estimation problem for a class of linear continuous-time systems under bit rate constraints. The data transmission between the sensors and the estimator is implemented through a digital communication network with limited bandwidth. By resorting to the singular value decomposition technique, an event-based encoding strategy is developed to encode the measurement signals into 1-bit codewords so as to reduce network resource consumption. The Zeno phenomenon is first proven to be excluded, and then a sufficient condition is established under which the decoding error is ultimately bounded. Subsequently, a necessary condition is proposed to derive a lower bound of the bit rate below which the decoding error diverges. Moreover, the explicit expression of the desired state estimator is parameterized and the boundedness of the estimation errors is also analyzed. Finally, two simulation examples are presented to validate the effectiveness of the proposed theoretical results.

Preview repetitive control with equivalent input disturbance for continuous‐time linear systems

This paper investigates the problem of preview repetitive control with equivalent-input-disturbance for a class of continuous-time linear systems in the presence of unknown external disturbances. First, an augmented delay system is constructed by using the nominal state equation with error system and the state equation of a modified repetitive controller, which is then transformed into a non-delayed one by state transformation. Next, by using optimal control theory, a preview repetitive control law is obtained. It is composed of state feedback, tracking error compensation, output of modified repetitive controller and preview compensation. Furthermore, in order to achieve a good disturbance estimation and attenuation performance, by applying the results of the standard equivalent-input-disturbance theory, a preview repetitive control law with equivalent-input-disturbance is offered for the uncertain system with unknown external disturbance. Finally, the numerical simulation example is provided to illustrate the effectiveness of the proposed method.

Predictor-based Disturbance Attenuation Control of a Class of Continuous-time Linear Systems with Input Delay

Predictor-based Disturbance Attenuation Control of a Class of Continuous-time Linear Systems with Input Delay

Observer-based robust exponential stabilization for linear systems with parameter uncertainties

This paper is concerned with the robust observer-based control problem for a class of continuous-time linear systems with parameter uncertainties. A less conservative approach is provided to deal with the quadratic terms involving in the Lyapunov stability analysis for the estimation error dynamic system. Sufficient conditions that ensure the exponential stability of the closed-loop system are established and formulated in terms of linear matrix inequalities. The obtained results are less conservative than some existing ones in recent literature. Finally, two numerical examples are given to show the validity and superiority of the proposed observer-based robust controller.

Sliding Mode Preview Control for a Class of Continuous-Time Linear Systems

In this paper, the sliding mode preview control problem for a class of continuous-time linear systems is studied. Firstly, an extended error system consisting of the error equation and the state equation of the original system is constructed, and the tracking problem is transformed into the regulation problem. Secondly, a quadratic performance index function is introduced for the state variables of the extended error system, and the preview sliding surface is designed based on the existing conclusions of the optimal preview control. Thirdly, the sliding mode controller with preview effect for the extended error system is designed by using the reaching law method; then, the desired sliding mode preview controller of the original system can be obtained through the integral. The numerical simulation verifies the feasibility of the proposed method.

Finite-time Extended State Observer Based Adaptive Optimal Control of Continuous-time Linear Systems

In this paper, a novel strategy iterative method based on finite-time extended state observer is proposed to find the online adaptive optimal controller for a class of linear continuous-time systems with completely unknown system dynamics and unmeasurable state variables. In this method, finite-time state observer estimates the system state variables by using the input and output information of the system and the policy iterative method uses the estimated state variables and system input information to iteratively solve the algebraic Riccati equation until the adaptive optimal controller is obtained. It is worth noting that the method proposed in this paper only uses the input and output information of the system, without requiring the apriori knowledge of the system matrices and the state variables. A numerical simulation example will be provided to demonstrate the effectiveness of the method.

Further refinement on controller design for linear systems with input saturation

This paper addresses on the design problem for a class of continuous-time linear systems under the saturated linear feedbacks. The concerned problem becomes an exponential stabilization one through the further refined treatment on the saturation nonlinearity, including a property of absolute value and the S-procedure lemma. Then, sufficient linear matrix inequality (LMI) conditions for its local exponential stabilizability are derived in the sense of Lyapunov stability criterion. A numerical example is provided to show the reduced conservatism of the proposed design conditions.

Robust control under constraints of linear systems with Markovian jumps

The object of this paper is to study the problem of robust stabilizability for a class of continuous-time Linear Systems with Markovian Jumps (LSMJ) and saturated input. Sufficient conditions for stochastic stabilizability with constrained control input are given in terms of Linear Matrix Inequalities (LMIs). The approach gives a direct expression of the linear state feedback controller that respects the condition of saturation. Also, the robustness of these systems for four types of structural uncertainties: (1) matching conditions, (2) norm bounded, (3) value bounded and (4) linear combinations is treated. Finally, numerical examples are given to illustrate the usefulness of the proposed results.

Non-uniform sampling finite-time control for networked control systems via event-driven transmission

This article investigates the networked finite-time control problem for a class of continuous-time linear systems. A novel event-driven data transmission scheme is invoked to reduce the network loads. Moreover, the non-uniform sampling triggered by sampling jitter or the fault of hold circuits is taken into account. By employing an input-delay approach, the underlying system is first reformulated to linear system with time-varying delays. Based on the Lyapunov–Krasovskii functional method, the stabilizing controller is then designed in the finite-time control sense, such that the closed-loop system is finite-time bounded. Potential and advantage of the developed techniques are demonstrated by a numerical example and an application to damping boring bar system.

Design of a Backstepping Tracking Controller for a Class of Linear Systems with Actuator Delay

This paper presents a method for designing a backstepping tracking controller for a class of continuous-time linear systems with actuator delay subject to a reference signal. The actuator delay can be modeled by a first-order hyperbolic PDE, and then a PDE-ODE coupled system is obtained. By applying the backstepping transformation to the coupled system, a feedback controller that includes the state of the system, the integral of the input control, and the integral of the tracking error is derived. We show that the closed-loop system is asymptotically stable at the equilibrium point and achieves complete regulation under the stabilizability assumption. The designs in this paper are illustrated with numerical simulations.

Robust Adaptive Control for a Class of Systems with Deadzone Nonlinearity

This paper presents a robust adaptive control scheme for a class of continuous-time linear systems with unknown non-smooth asymmetrical deadzone nonlinearity at the input of the plant. The methodology is applied to handle input deadzone as well as unmeasurable disturbances simultaneously in strictly matched systems. The proposed controller robustly cancels any residual distortion caused by the inaccurate deadzone cancellation scheme. The scheme is shown to successfully cancel the deadzone’s deleterious effect as well as eliminate other unmeasurable disturbances within the span of the input. The new controller ensures the global stability of all states and adaptations, and achieves asymptotic tracking. The asymptotic stability of the closed-loop system is proven by Lyapunov arguments, and simulation results confirm the efficacy of the control methodology.

Delay-dependent Stabilization Conditions of Controlled Positive Continuous-time Systems

The stabilization problem for a class of linear continuous-time systems with time-varying non differentiable delay is solved while imposing positivity in closed-loop. In particular, the synthesis of state-feedback controllers is studied by giving sufficient conditions in terms of linear matrix inequalities (LMIs). The obtained results are then extended to systems with non positive delay matrix by applying a memory controller. The effectiveness of the proposed method is shown by using numerical examples.

Robust H∞ Filter Design for Time-delay Systems with Saturation

This paper investigates the H ? filtering problem for a class of linear continuous-time systems with both time delay and saturation. Such systems have time delay in their state equations and saturation in their output equations, and their process and measurement noises have unknown statistical characteristics and bounded energies. Based on the Lyapunov-Krasovskii stability theorem and the linear matrix inequalities (LMIs) technique, a generalized dynamic filter architecture is proposed, and a filter design method is developed. The linear H ? filter designed by the method can guarantee the H ? performance. The parameters of the designed filter can be obtained by solving a kind of LMI. An illustrative example shows that the design method proposed in this paper is very effective.

Fixed-Interval Smoothing for Linear Impulsive Systems with a Class of H<sub>∞</sub> Criteria

In this paper we study the H∞ smoothing problem for a class of linear continuous-time systems with impulsive effects and Gaussian white noises. We adopt the forward-backward filtering theory as a solution of this problem. Two types of Riccati differential equations depend on the H∞ bound, i.e., γ value. The theory presented in this paper can be restricted to the one for discrete-time systems. Finally we give numerical examples.

Fixed-Interval Optimal Smoothing for Linear Impulsive Systems

In this paper we study the fixed-interval optimal smoothing problems for a class of linear continuous-time systems with impulsive effects. We adopt a maximum likelihood (ML) approach and derive a maximum likelihood noncausal estimator on the fixed time interval. We derive an extension of the Fraser's algorithm for the linear discrete-time smoother to the impulsive systems utilizing the filtering theory of the impulsive systems.

Adaptive Backstepping Controller Design for Stochastic Jump Systems

In this technical note, we improve the results in a paper by Shi et al., in which problems of stochastic stability and sliding mode control for a class of linear continuous-time systems with stochastic jumps were considered. However, the system considered is switching stochastically between different subsystems, the dynamics of the jump system can not stay on each sliding surface of subsystems forever, therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this technical note, the backstepping techniques are adopted to overcome the problem in a paper by Shi et al.. The resulting closed-loop system is bounded in probability. It has been shown that the adaptive control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. A numerical example is given to show the potential of the proposed techniques.

Efficient parameterisation to stability and feedback synthesis of linear time-delay systems

In this study, we provide efficient solution to the problems of delay-dependent analysis and feedback synthesis for a class of linear continuous-time systems with time-varying delays. An augmented Lyapunov functional is properly constructed and an improved free-weighting method is deployed to exhibit the delay-dependent dynamics. Delay-dependent stability analysis is then performed to develop linear matrix inequalities (LMIs)-based conditions under which the linear delay system is asymptotically stable with an γ-level ℒ2 gain. The superiority of the developed method in comparison with other existing methods is established. By delay-dependent feedback synthesis, we design state-feedback and dynamic output-feedback schemes to guarantee that the closed-loop system enjoys the delay-dependent asymptotic stability with a prescribed γ-level ℒ2 gain. Extension to systems with convex-bounded parameter uncertainties in all system matrices is also provided. All the developed results are tested on representative examples.