Linear Time-varying Systems Research Articles

High-Confidence Data-Driven Ambiguity Sets for Time-Varying Linear Systems

High-Confidence Data-Driven Ambiguity Sets for Time-Varying Linear Systems

Uniform asymptotic and input to state stability by indefinite Lyapunov functions

In this work, we study uniform, uniform asymptotic, and input-to-state stability conditions for nonlinear time-varying systems. We introduce an easily verifiable condition for uniform attractivity by utilizing an indefinite sign upper bound for the derivative of the Lyapunov function. With this bounding structure, we propose novel conditions that enable us to test uniform stability, uniform asymptotic stability, and ISS, easily. As a result, the constraints on the coefficients of the bound that identify uniformity for stability and attractivity, and many of the available conditions have been relaxed. The results are also used for the perturbation problem of uniformly stable and uniformly asymptotically stable linear time-varying systems. Consequently, we demonstrate that uniform asymptotic stability of nonlinear time-varying systems can be robust for perturbations, but with special time-varying coefficients.

Retracted: Noise-Tolerant Zeroing Neural Dynamics for Solving Hybrid Multilayered Time-Varying Linear Equation System

Retracted: Noise-Tolerant Zeroing Neural Dynamics for Solving Hybrid Multilayered Time-Varying Linear Equation System

New Approach to Feedback Stabilization of Linear Discrete Time-Varying Stochastic Systems

New Approach to Feedback Stabilization of Linear Discrete Time-Varying Stochastic Systems

Novel closed-loop controllers for fractional linear quadratic time-varying systems

A novel method for finding the closed-loop optimal controllers of the finite-time fractional linear quadratic regulator systems is introduced. The necessary optimality conditions for the fractional optimal control problems are obtained. The matrix fractional differential Riccati equation is presented. A new method for solving the fractional differential Riccati equation is given for the first time which can also be applied to the integer order Riccati equation. Several illustrative examples (including a high order system) are presented to show the applicability and capabilities of the method.

Local Design of Distributed State Estimators for Linear Discrete Time-Varying Systems Over Binary Sensor Networks: A Set-Membership Approach

Local Design of Distributed State Estimators for Linear Discrete Time-Varying Systems Over Binary Sensor Networks: A Set-Membership Approach

Uniformity of Controllability and Stabilization of Switched Linear Time-varying Systems

Uniformity of Controllability and Stabilization of Switched Linear Time-varying Systems

Prediction method for closed-loop data for emulated linear time-varying system

In this study, data-driven control methods, namely VRFT, FRIT, and estimated response iterative tuning (ERIT), are proposed for controlled plants in linear systems. Notably, the ERIT method allows the prediction of input/output data in advance and the adjustment of feedforward controllers. A method is proposed in this study for predicting closed-loop data for an arbitrary controller with a linear and time-invariant system as the controlled plant.

Fast System Level Synthesis: Robust Model Predictive Control using Riccati Recursions

System level synthesis enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem for linear time-varying systems. The proposed algorithm iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of <img???> for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups by a factor of up to 103 compared to general-purpose commercial solvers.

Strong Lyapunov Functions for Linear Time-Varying Systems Under Persistency of Excitation

Strong Lyapunov Functions for Linear Time-Varying Systems Under Persistency of Excitation

Robustness analysis of uncertain time‐varying systems with unknown initial conditions

SummaryThis paper focuses on the robustness analysis of discrete‐time, linear time‐varying (LTV) systems subject to various uncertainties, such as static and dynamic, time‐invariant and time‐varying, linear perturbations, and unknown initial conditions. The proposed approach is based on integral quadratic constraint theory and allows for a potentially more accurate characterization of the set in which the initial state resides by imposing separate constraints on the initial values of the state variables as opposed to simply requiring the initial state to lie in some ellipsoid. The adopted problem formulation facilitates the analysis of uncertain LTV systems subject to disturbance inputs that are bounded pointwise in time, and the developed results enable determining useful pointwise bounds on the performance outputs given such inputs. The main analysis result is given for eventually periodic nominal systems, which include linear time‐invariant, finite horizon, and periodic systems as special cases. The analysis conditions are expressed as linear matrix inequalities. Two additional results stemming from the main analysis theorem are provided that can be used to determine overapproximated ellipsoidal reachable sets. Finally, the utility of the proposed approach is demonstrated in an illustrative example.

Feasibility analysis and saturation control for underactuated spacecraft formation reconfiguration in elliptic orbits

This work proposes a saturation control scheme for underactuated spacecraft formation reconfiguration in elliptic orbits without radial or along-track thrust. Firstly, the rank criterion method is applied to analyze the controllability and feasibility of formation reconfiguration by linearizing the linear time-varying dynamics to linear time-invariant ones. Based on the inherent coupling of the linear time-varying system, the underactuated error dynamics are presented for either underactuated case. Subsequently, the developed underactuated saturation controller can ensure that the time-varying system trajectory asymptotically converges to the specified configuration. The Lyapunov-based analysis presents the constraint conditions of controller parameters and the stable reconfiguration accuracy of the system states. Finally, numerical simulations for both underactuated scenarios are performed in the environment with J2 perturbation to verify the validity of the proposed underactuated control scheme.

Hierarchy of Quadratic Lyapunov Functions for Linear Time-Varying and Related Systems

A method for constructing homogeneous polynomial Lyapunov functions is presented for linear time-varying or switched-linear systems and the class of nonlinear systems that can be represented as such. The method uses a simple recursion based on the Kronecker product to generate a hierarchy of related dynamical systems, whose first element is the system under study and the second element is the well-known Lyapunov differential equation. It is then proven that a quadratic Lyapunov function for the system at one level in the hierarchy, which can be found via semidefinite programming, is a homogeneous polynomial Lyapunov function for the system at the base level in the hierarchy. Searching for Lyapunov functions of the foregoing kind is equivalent to searching for homogeneous polynomial Lyapunov functions via the formulation of sum-of-squares programs. The quadratic perspective presented in this paper enables the easy development of procedures to compute bounds on pointwise-in-time system metrics, such as peak norms, system stability margins, and many other performance measures. The applications of the theory to analyzing an aircraft model, on the one hand, and an experimental aerospace vehicle, on the other hand, are presented. The theory can be comprehended with a first course on state-space control systems and an elementary knowledge of convex programming.

Dynamic learning from adaptive neural control for full-state constrained strict-feedback nonlinear systems

This study focuses on the learning and control issues of strict-feedback systems with full-state constraints. To achieve learning capability under constraints, transformation mapping is utilized to convert the original system with full-state constraints into a quasi-pure-feedback unconstrained system. Utilizing the system transformation technique, only a single neural network (NN) is required to identify the unknown dynamics within the transformed system. Combining the dynamic surface control design, a novel adaptive neural control scheme is developed to ensure that all closed-loop signals are uniformly bounded, and every system state remains within the predefined constraint range. In addition, the precise convergence of NN weights is further transformed into an exponential stability problem for a category of linear time-varying systems under persistent excitation conditions. Subsequently, the converged NN weights are efficiently stored and utilized to create a learning controller to achieve better control performance while abiding by the full-state constraints. The viability of this control strategy is demonstrated via simulations.

Stability of conformable fractional time-varying linear systems

In this paper, we investigate the exponential and asymptotic stability analysis of conformable fractional linear time-varying systems. We propose sufficient conditions for testing the asymptotic and exponential stability of conformable differential systems by using the notion of stable functions and differential Lyapunov inequalities. Furthermore, we apply the developed approach to the problem of conformable stabilisation and observer design for conformable fractional linear time-varying systems.

On the minimum energy compensation for linear time-varying disturbed systems

On the minimum energy compensation for linear time-varying disturbed systems

Event-triggered aperiodic intermittent control for linear time-varying systems

This paper considers the aperiodic intermittent control (AIC) for linear time-varying systems (LTVSs), where the occurrence instants are determined by an event triggering mechanism based on Lyapunov functions. For LTVSs, most of the existing results are demanded that the feedback controls are exerted all the time. In fact, in many practical applications, the applied controls are unnecessary/impossible to be imposed all the time. Therefore, the event-triggered AIC is introduced in this paper for LTVSs, and the uniformly stability, globally asymptotic stability and finite-time stability are proposed for LTVSs with event-triggered AIC, respectively. In addition, by using the piecewise constant feedback control method, effective intermittent controllers are designed for LTVSs. Finally, we present two numerical examples to illustrate the efficacy of the derived results.

New formulations and experimental validation of non-stationary convolutions for the fast simulation of time-variant flowrates in ground heat exchangers

Flowrate control can have a significant positive impact on the thermal performance and economic profitability of ground-source heat pump systems. Including dynamic advective processes in the design phase, however, remains a challenging task, as few computationally efficient modeling tools allow for their adequate and accurate representation. The present work addresses this issue by presenting new formulations of non-stationary convolutions, an efficient simulation algorithm that relies on the theory of linear time-variant systems for predicting the thermal response of a ground heat exchanger to both dynamic heat loads and flow rates. First, the new original formulations are presented, which include (1) a simple time-domain expression and (2) a fast frequency-domain expression. Then, the efficiency and validity of the new formulations are verified using experimental multi-flowrate thermal response tests involving dynamic circulation, pumping and bleed flow rates in closed-loop and standing column well ground heat exchangers. Results show that the new formulations can reproduce the outlet fluid temperature of both experimental test cases with good accuracy ( MAE = 0.06 ∘ C and 0.26 ∘ C , respectively). At last, the high efficiency of the new frequency-domain expression is demonstrated, with the computing times ( 0.04 s and 0.01 s ) being 100 and 8 times faster than the original formulation in both scenarios.

Finite Horizon Worst Case Analysis of Linear Time-Varying Systems Applied to Launch Vehicle

This article presents an efficient approach to compute the worst case gain of the interconnection of a finite time horizon linear time-varying system and a perturbation. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQCs). A condition for the worst case gain of such an interconnection can be formulated using dissipation theory as a parameterized Riccati differential equation, which depends on the chosen IQC multiplier. A nonlinear optimization problem is formulated to minimize the upper bound of the worst case gains over a set of admissible IQC multipliers. This problem can be efficiently solved with a custom-tailored logarithmically scaled, adaptive differential evolution algorithm. It provides a fast alternative to similar approaches based on solving semidefinite programs. The algorithm is applied to the worst case aerodynamic load analysis of an expendable launch vehicle (ELV). The worst case load of the uncertain ELV is calculated under wind turbulence during the atmospheric ascend and compared to results from nonlinear simulation.

Distributed exponential state estimation of linear systems over jointly connected switching networks

Recently, the distributed state estimation problem for continuous-time linear systems over jointly connected switching networks was solved. Due to the use of the generalized Barbalat’s Lemma, it can only show that the estimation errors asymptotically converge to the origin. By a completely different approach, this paper further studies the distributed state estimation problem with two new features. First, the asymptotic convergence is strengthened to the exponential convergence. This strengthened result not only offers a guaranteed convergence rate, but also renders the error system total stability and thus the capability to withstand small disturbances. Second, the coupling gains of our local observers can be different from each other and thus offers greater design flexibility, while the coupling gains in the existing result were required to be identical. These two new features are achieved by establishing exponential stability for two classes of linear time-varying systems, which may have other applications.