Control Of Time-varying Systems Research Articles

Special issue on monitoring and control of time-varying systems with cyber-physical interactions

Special issue on monitoring and control of time-varying systems with cyber-physical interactions

Adaptive robust integrated guidance and control for thrust-vector-controlled aircraft by solving LQR online

In order to enhance the matching relationship between guidance subsystem and control subsystem of the thrust-vector-controlled aircraft, a kind of sufficient modeling and adaptive robust design facing to integrated guidance and control (IGC) is proposed. With respect to the researched aircraft, a linear state-dependent mathematical model facing to IGC design is first established. Based on the as-built model, a new kind of adaptive robust IGC law is proposed and it is composed by an adaptive optimal IGC law and a robustness-improved IGC law. In order to guarantee the global stability of time-varying control system, the adaptive optimal IGC law is designed by solving Riccati matrix equation on line and using matrix Sign function method. Furthermore, in order to enhance the robust ability against the unmatched system uncertainties, the robustness-improved IGC law is designed by using dynamic surface control approach and extended state observing strategy. Simulation results present that, the proposed IGC scheme presents more performance advantages compared with traditional IGC schemes, including the improvement of guidance precision and attitude stabilization. Furthermore, in the conditions of 256 simulation combinations, the minimum relative distances between aircraft position and target position are distributed from 0.103m to 5.333m, and the average value is 2.208m, which means the proposed IGC scheme possesses strong robustness against different and time-varying model uncertainties.

Compound Control Design of Near-Space Hypersonic Vehicle Based on a Time-Varying Linear Quadratic Regulator and Sliding Mode Method

The design of a hypersonic vehicle controller has been an active research field in the last decade, especially when the vehicle is studied as a time-varying system. A time-varying compound control method is proposed for a hypersonic vehicle controlled by the direct lateral force and the aerodynamic force. The compound control method consists of a time-varying linear quadratic regulator (LQR) control law for the aerodynamic rudder and a sliding mode control law for the lateral thrusters. When the air rudder cannot continuously produce control force and torque, the direct lateral force is added to the system. To solve the problem that LQR cannot directly obtain the analytical solution of the time-varying system, a novel approach to approximate analytical solutions using Jacobi polynomials is proposed in this paper. Finally, the stability of the time-varying compound control system is proven by the Lyapunov–Krasovskii functional (LKF). The simulation results show that the proposed compound control method is effective and can improve the fast response ability of the system.

Flying qualities based time-varying stability augmentation system design for tiltrotor conversion control

Tiltrotors have three flight modes that pose control problems and quality defects during the conversion process. To address this, a novel flying qualities-based time-varying stability augmentation system is designed to achieve multi-mode, nonlinear, and time-varying stability. The system integrates a nonlinear time-varying control law with the flying qualities requirements for all three flight modes. It consists of an inner and outer loop control framework, where the control law in the inner loop is designed based on the Lyapunov theorem of stability. The reference models in the outer loop are derived from the flying qualities criteria to meet level one flying qualities requirements. To evaluate the conversion process, a time-varying flying qualities evaluation method is developed, which includes the conversion path, pilot model, and time-varying flying qualities index. The proposed time-varying stability augmentation control system is then tested through simulation during the conversion process. A pilot-aircraft closed-loop system is established for conducting experiments. Comparison between simulation results and pilot-in-loop experiment results demonstrates the effectiveness of the proposed control system. Furthermore, it proves that the evaluation method is suitable for analyzing time-varying systems. This research can be valuable in designing and evaluating stability augmentation controls for strongly time-varying systems.

Finite-Time Guaranteed-Cost H∞ Control of Time-Varying Systems With Actuator Saturation Based on Memory Dynamic Event-Triggered Mechanism

Finite-Time Guaranteed-Cost H_∞ Control of Time-Varying Systems With Actuator Saturation Based on Memory Dynamic Event-Triggered Mechanism

Robust Sliding Mode Control for Time-Varying Systems With Adaptive Prescribed Performance

Robust Sliding Mode Control for Time-Varying Systems With Adaptive Prescribed Performance

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

In modern control theory applications, input–output feedback often arises and plays a crucial role in stabilizing any target control systems. However, in many practical applications, the knowledge of full information on the state of systems may not be available in general due to measurements. In order to control such types of systems, this paper uses a universal concept of real order calculus to stabilize by the method of dynamic output feedback control. Is it possible to design a dynamic output feedback stabilization for time-varying real order control systems? This work develops a new dynamic output feedback control method and proposes linear homogeneous time-varying control law to stabilize incommensurate nonlinear time-varying real order systems under the action of Caputo derivative with an addendum of ultimate random initial-time. We utilize the ideas of the comparison method and establish order-dependent asymptotic results associated with uniform Lipschitz continuous functions that provide stabilization by means of the dynamic output state feedback control method. We provide three examples that include a practical system and show the importance of some theoretical results in the demonstration to stabilize the problems by means of proposed control method.

Input-Output Finite-Time Guaranteed Cost Control for Time-Varying Systems Based on an Aperiodic Adaptive Event-Triggered Mechanism

Input-Output Finite-Time Guaranteed Cost Control for Time-Varying Systems Based on an Aperiodic Adaptive Event-Triggered Mechanism

Topological equivalence of linear time-varying control systems

Abstract In this paper, we mainly studied the topological equivalence of linear time-varying (LTV) control system $\dot{x}\left ( t\right )=A(t)x(t)+B(t)u(t)$ defined on an interval $I \subset \mathbb{R}^{+}$. After giving a new definition of the topological equivalence, we investigated the local equivalence of LTV control systems under two new hypotheses. These hypotheses were made by the local behavior of Krylov indices (which turned out to be controllability indices for the linear time-invariant (LTI) control systems). It was found out that Krylov indices play an important role in the classification problem of LTV control systems. Compared with our former work on the topological equivalence of LTI control systems, new methods and techniques were taken to deal with new difficulties occurred for LTV control systems.

Fixed-time adaptive fuzzy control for time-varying systems based on nominal substitution

Fixed-time adaptive fuzzy control for time-varying systems based on nominal substitution

Feedback-aided PD-type iterative learning control for time-varying systems with non-uniform trial lengths

In most implementations of iterative learning control (ILC) for trajectory tracking, it is usually required that the trial lengths of different iterations are uniform. However, this requirement may not always be ensured in practical applications. In this paper, a feedback-aided PD-type ILC design for time-varying systems with non-uniform trial lengths is proposed. Although the actual trial lengths are non-uniform, the designed update sequences provide uniform full-length signals for the update process. Meanwhile, information from the most recent valid iterations can be better used than the mechanisms that compensate with hypothesized data, such as zero. Their recursive generation also reduces the storage burden compared to search strategies. The feedback error signal can be additionally used as part of the correction term to improve the system performance compared to the traditional open-loop approaches. Under a deterministic model, the main convergence results are obtained by combining the [Formula: see text]-norm technique with the inductive analysis approach. At last, a linear numerical simulation and a nonlinear single-joint robot simulation are performed, respectively, to show that the proposed design can achieve the asymptotic tracking of the desired trajectories for time-varying systems with non-uniform trial lengths.

Strong Observability of LTV Systems With Feedthrough and On-Orbit Reconnaissance and Evasion Applications

This letter considers linear time-varying control systems with feedthrough. A necessary and sufficient condition for strong observability (also known as observability with unknown inputs) is stated in terms of the observability matrix and newly redefined invertibility matrix. This is followed by an observer for pointwise reconstruction of the state from the output and its time derivatives. A variable-time weakly unobservable subspace is then introduced such that the rank test can be recast in terms of this subspace and the kernel of a certain matrix. The subspace characterization leads to results on the existence and construction of unobservable state and control functions. The theoretical results are illustrated in an on-orbit reconnaissance application. Within the context of a time-varying relative orbital motion model, it is shown that strong observability is satisfiable with any constant or bounded feedthrough matrix. In the absence of strong observability, control functions to evade observation are constructed.

Parameter Estimation in Adaptive Control of Time-Varying Systems Under a Range of Excitation Conditions

This article presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error trajectories to tend exponentially fast toward a compact set whenever excitation conditions are satisfied. This algorithm is employed in a large class of problems where unknown parameters are present and are time-varying. It is shown that this algorithm guarantees global boundedness of the state and parameter errors of the system, and avoids an often used filtering approach for constructing key regressor signals. In addition, intervals of time over which these errors tend exponentially fast toward a compact set are provided, both in the presence of finite and persistent excitation. A projection operator is used to ensure the boundedness of the learning rate matrix, as compared to a time-varying forgetting factor. Numerical simulations are provided to complement the theoretical analysis.

Control of time-varying systems based on forward Riccati formulation in hybrid functions domain

In this paper, the time-varying system control is resolved with the aid of forward Riccati formulation and hybrid functions. The applied Riccati equations need neither advanced knowledge of the system dynamics nor the assumption of the future information of system matrices. Herein, the state space equation of LTV system is rewritten in the Hybrid functions (HF) domain where results a set of linear discrete equations instead of having a complex Forward-in-time Propagating Riccati Equation (FPRE). The HF evolve from the synthesis of sample-and-hold functions (SHF) and triangular functions (TF) that can estimate any functions based on the summation of two series. The feasibility of the proposed method is investigated by various numerical control cases. Numerical results demonstrated that the proposed method is usable in both periodic and non-periodic systems with less control effort and significant damping time.

Sliding Mode Control of Networked Control Systems: An Auxiliary Matrices-Based Approach

A novel sliding mode control design method is developed to address the robust stabilization problem for uncertain time-varying networked control systems subject to state delay, which utilizes auxiliary matrices to avoid the difficulties of finding quadratic Lyapunov functions and solving the linear matrix inequalities. By embedding the original system into a higher dimensional system, simplified piecewise nonnegative functions can be used to analyze the system. Stability criteria are obtained which can be satisfied and verified easily. An optimization problem is defined based on these criteria, to obtain the sliding mode control parameters to ensure the exponential stability of the closed-loop system.

A novel strategy for identification and control of a class of linear systems

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.

Robust adaptive event-triggered fault-tolerant control for time-varying systems against perturbations and faulty actuators

In this paper, the robust adaptive event-triggered fault-tolerant control (FTC) problem is addressed for a time-varying continuous-time system with perturbations and general actuator failures. In order to eliminate the adverse effects of faults and perturbations on system performance, a robust fault-tolerant controller is derived via integrating direct adaptive control technique to adjust control parameters. For the sake of reducing the communication resources and actuator actions, an event-triggered control technique is presented to adjust the control inputs based on the proposed FTC strategy. To ensure the system is free from Zeno phenomenon, a bound on the inter-event execution time is established. On the basis of the event-trigger condition, the uniformly bounded stability results of the adaptive FTC system are obtained by utilizing Lyapunov stability theory in the presence of actuator failures and perturbations. The superior of the developed control strategy is substantiated by simulation results of a rocket fairing system.

Overapproximating Reachable Tubes of Linear Time-Varying Systems

We present a method to over-approximate reachable tubes over compact time-intervals, for linear continuous-time, time-varying control systems whose initial states and inputs are subject to compact convex uncertainty. The method uses numerical approximations of transition matrices, is convergent of first order, and assumes the ability to compute with compact convex sets in finite dimension. We also present a variant that applies to the case of zonotopic uncertainties, uses only linear algebraic operations, and yields zonotopic over-approximations. The performance of the latter variant is demonstrated on an example.

Dynamic Behavior Analysis and Stability Control of Tethered Satellite Formation Deployment.

In recent years, Tethered Space Systems (TSSs) have received significant attention in aerospace research as a result of their significant advantages: dexterousness, long life cycles and fuel-less engines. However, configurational conversion processes of tethered satellite formation systems in a complex space environment are essentially unstable. Due to their structural peculiarities and the special environment in outer space, TSS vibrations are easily produced. These types of vibrations are extremely harmful to spacecraft. Hence, the nonlinear dynamic behavior of systems based on a simplified rigid-rod tether model is analyzed in this paper. Two stability control laws for tether release rate and tether tension are proposed in order to control tether length variation. In addition, periodic stability of time-varying control systems after deployment is analyzed by using Floquet theory, and small parameter domains of systems in asymptotically stable states are obtained. Numerical simulations show that proposed tether tension controls can suppress in-plane and out-of-plane librations of rigid tethered satellites, while spacecraft and tether stability control goals can be achieved. Most importantly, this paper provides tether release rate and tether tension control laws for suppressing wide-ranging TSS vibrations that are valuable for improving TSS attitude control accuracy and performance, specifically for TSSs that are operating in low-eccentricity orbits.

Solution of Time-Varying Index-2 Linear Differential Algebraic Control Systems Via A Variational Formulation Technique

This paper deals with finding an approximate solution to the index-2 time-varying linear differential algebraic control system based on the theory of variational formulation. The solution of index-2 time-varying differential algebraic equations (DAEs) is the critical point of the equivalent variational formulation. In addition, the variational problem is transformed from the indirect into direct method by using a generalized Ritz bases approach. The approximate solution is found by solving an explicit linear algebraic equation, which makes the proposed technique reliable and efficient for many physical problems. From the numerical results, it can be implied that very good efficiency, accuracy, and simplicity of the present approach are obtained.