Sampled-data State Feedback Control Research Articles

Data-driven NODE based multirate sampled data state feedback control

In control systems, multirate sampled data systems are widely used because they improve system performance and adaptability, especially when systems deal with both continuous and discrete signals or entirely asynchronous sampling signals. This paper addresses the challenges of system stability and optimization in these multirate systems, specifically for a certain class of nonlinear systems. Existing controllers, though capable in certain contexts, tend to be overly complex and often lack guidance on appropriate sampling interval selection for these intricate systems. Our approach takes into account both system stability and practical considerations, providing a criterion for selecting multiple sample periods that guarantees system stability, as well as an optimal choice of parameters by Neural Ordinary Differential Equation (NODE) for the linear practical controller that maximizes performance according to a predefined performance index. With the construction of a set of linear stabilizers that are implemented using multirate sampled data, the stability and controller design at three different sampling levels are studied. To demonstrate the effectiveness of our proposed strategy, the simulations and real world application of a single-link robot system are presented.

Sampled-data state feedback control design for evolutionary threshold public goods games on coupled networks

Sampled-data state feedback control design for evolutionary threshold public goods games on coupled networks

LMIs-based exponential stabilization for interval delay systems via congruence transformation: Application in chaotic Lorenz system

This paper investigates the stochastic Takagi-Sugeno (T-S) fuzzy uncertainty-dependent state feedback sampled-data control, asymptotical stability and exponential stability analysis for a class of stochastic T-S fuzzy system with measurable uncertainties, mixed interval time varying delays and Gaussian white noise. Firstly, the T-S fuzzy model and stochastic Bernoulli theory are employed to approximate the system plant. Secondly, the stochastic T-S fuzzy uncertainty-dependent state feedback sampled-data controller is designed via uncertainty-dependent parameters and the hold times series of sampled-data. Thirdly, the Bernoulli probability distribution is employed to describe the random occurrence characteristic of multipath packet dropouts. Three classes of delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) are derived for the closed-loop system. The multiple integral fuzzy-basis-dependent Lyapunov functional and augmented state variable are employed to derive the delay-dependent stability conditions, then the closed-loop system is asymptotically stable and exponentially stable. The congruence transformation method and prescribed H-infinity performance functional are employed to derive the less conservative delay-dependent stability conditions, and the prescribed H-infinity performance is guaranteed. The relaxation matrix and congruence transformation method are employed to design the linear transformation equalities and congruence transformation matrices, then the controller gain matrix is determined and computation complexity of solving LMIs is reduced. Finally, the proposed method is applied in the chaotic Lorenz system to show the effectiveness and advantage of proposed method.

Output Regulation of Switched Stochastic Systems with Sampled-Data Control

This paper studies the output regulation problem for a class of switched stochastic systems with sampled-data control. Solutions to the output regulation problem are given in two situations. On the one hand, the exogenous signal is assumed to be a constant. By designing a sampled-data state feedback controller, we obtain that the closed-loop system is mean-square exponentially stable and the regulation output tends to zero. On the other hand, the exogenous signal is assumed to be time-varying with bounded derivative. By constructing a class of Lyapunov-Krasovskii functional and a switching rule which satisfies the average dwell time, sufficient conditions for the solvability of practical output regulation problem are given for switched stochastic systems. Finally, numerical examples are given to illustrate the effectiveness of the method.

Lebesgue sampling approach to robust stabilization of boolean control networks with external disturbances

This paper introduces the Lebesgue sampling approach to the robust stabilization of Boolean control networks (BCNs) with external disturbances. Given a Lebesgue sampling region and a feedback control, a time aggregated system is obtained via the semi-tensor product method. Then, a new criterion is presented for the robust stabilization of time aggregated system. Furthermore, given a signal of Lebesgue sampling, a sequence of the Lebesgue type robust reachable sets is constructed. Based on these reachable sets, several algorithms are presented to design both Lebesgue sampling region and sampled-data state feedback control for the robust stabilization of BCNs.

Event-triggered stabilisation of sampled-data singular systems: a hybrid control approach

This paper provides a design of event-triggered feedback stabilisation scheme for a class of sampled-data singular systems, in which the input matrix corresponding to the algebraic equation is not full column rank. First, unlike the conventional piecewise-constant sampled-data feedback controller, a novel hybrid impulsive and sampled-data state feedback controller is designed, which can effectively match with the algebraic equation at sampling instants. An improved discrete event-triggering mechanism with checking period is proposed to achieve exponential stabilisation. Based on these, by applying the input delay approach and defining a new input-delay dependent Lyapunov functional, a sufficient stability condition is presented which ensures that the solution of the event-triggered control system exists and is unique, and the system is exponentially stable with definite decay rate. The estimate of decay coefficient is also given explicitly. Then, an optimisation-based method is developed to jointly design the hybrid controller gains and the event parameters. Finally, two simulation examples including a linearised 2-generator and 6-bus power network system are given to illustrate the validity of the new approach.

Digital control of a family of time-delay feedforward systems with sparse sampling

For a family of time-delay feedforward systems satisfying a linear growth condition, we study the problem of global asymptotic stabilization by digital state and output feedback, respectively, under arbitrarily sparse sampling. Using the Lyapunov–Krasovskii functional method and the feedback domination design, we construct memoryless sampled-data state and/or output feedback controllers that achieve global asymptotic stability of the hybrid closed-loop systems with large delays. Applications of the sampled-data control schemes are demonstrated through an example with simulations.

Sampled-data control design for systems with quantized actuators

This paper deals with the problem of designing a sampled-data state feedback control law for continuous-time linear control systems subject to uniform input quantization. The sampled-data state feedback is designed to ensure uniform global asymptotic stability (UGAS) of an attractor surrounding the origin. The closed-loop system is rewritten as a hybrid dynamical system. To do this, an auxiliary clock variable triggering the occurrence of sampling events is introduced. A numerically tractable algorithm with feasibility guarantees, based on concave-convex decomposition, is then proposed allowing to minimize the size of the attractor. Theoretical results are illustrated in a numerical example.

Stability analysis and stabilization of LPV systems with jumps and (piecewise) differentiable parameters using continuous and sampled-data controllers

Linear Parameter-Varying (LPV) systems with jumps and piecewise differentiable parameters is a class of hybrid LPV systems for which no tailored stability analysis and stabilization conditions have been obtained so far.11Except, of course, in the conference version of this work. We fill this gap here by proposing an approach based on a clock- and parameter-dependent Lyapunov function yielding stability conditions under both constant and minimum dwell-times. Interesting adaptations of the latter result consist of a minimum dwell-time stability condition for uncertain LPV systems and LPV switched impulsive systems. The minimum dwell-time stability condition is notably shown to naturally generalize and unify the well-known quadratic and robust stability criteria all together. Those conditions are then adapted to address the stabilization problem via timer-dependent and a timer- and/or parameter-independent (i.e. robust) state-feedback controllers, the latter being obtained from a relaxed minimum dwell-time stability condition involving slack-variables. Finally, the last part addresses the stability of LPV systems with jumps under a range dwell-time condition which is then used to provide stabilization conditions for LPV systems using a sampled-data state-feedback gain-scheduled controller. The obtained stability and stabilization conditions are all formulated as infinite-dimensional semidefinite programming problems which are then solved using sum of squares programming. Examples are given for illustration.

Sampled-data control of Lur’e systems

The main purpose of this paper is to fill a gap in the literature concerning the problem of designing a sampled-data control law for continuous-time Lur’e systems. The goal is to design a state feedback sampled-data control for this class of nonlinear systems preserving global asymptotic stability and minimizing a guaranteed quadratic cost. The main challenge towards the solution of the proposed problem is to handle this class of nonlinear system in order to propose less conservative design conditions expressed through differential linear matrix inequalities - (DLMIs). Bellman’s Principle of Optimality applied together with the Popov–Lyapunov function that emerges from the celebrated Popov Stability Criterion is the key issue to obtain the reported results. Two examples are solved for illustration.

Optimal Asynchronous Stabilization for Boolean Control Networks With Lebesgue Sampling.

Using semitensor products (STPs) of matrices, sampled-data state-feedback control (SDSFC) with the Lebesgue sampling region Sτ is first considered to stabilize a Boolean control network (BCN) to a fixed point, under which a necessary and sufficient condition for stabilization is obtained when the considered BCN with the Lebesgue sampling region is converted to a switching system. Meanwhile, the corresponding asynchronous SDSFC gains are designed from a sequence of reachable sets. Then, an algorithm is shown to obtain the minimal number of controlling times and all states globally stabilize to the desired state with the fastest convergence rate under the minimal number of controlling times. Besides, the results have been extended to p Lebesgue sampling regions Sτi, i=1,2,…, p . And some results are presented for this situation, including the necessary and sufficient conditions stabilization under the p Lebesgue sampling regions, the asynchronous SDSFC gains, and the algorithm to obtain the optimal states sampling regions. Examples are listed to show the effectiveness of our results, and the biological example indicates that the SDSFC with Lebesgue sampling is also suitable for stochastic BCNs.

Global sampled-data stabilization for a class of nonlinear systems with arbitrarily long input delays via a multi-rate control algorithm

In this paper, the problem of global sampled-data stabilization is investigated for high-order nonlinear systems with arbitrarily long input delays. Based on the Lie algebra technique in nonlinear control theory, a discrete-time predictor-based multi-rate sampled-data state feedback control law with a series expansion form is proposed to ensure that the resulting system is globally asymptotically stable under some conditions. Compared with the existing methods, the proposed control algorithm just needs to know the approximate prediction of state variables, and the faster decrease of Lyapunov function may be provided for each subsystem. Performance of approximate versions of the proposed controller is given by theoretical analyses. It is showed that the approximate controllers achieve practical stability of the sampled-data closed-loop system. Finally, the obtained stabilization results are applied to a trajectory tracking problem for a high-order planar system.

Fault tolerant sampled-data [formula omitted] control for networked control systems with probabilistic time-varying delay

In this study, the problem of fault-tolerant sampled-data H∞ control for a networked control system with random time delays and actuator faults is investigated. Stochastic variables conforming with the Bernoulli distribution are considered to depict random time delays. A state feedback sampled-data controller is designed to ensure the asymptotical stability and H∞ performance of the resulting closed-loop system. By applying the Lyapunov–Krasovskii stability theory and the reciprocally convex combination lemma, a stability criterion for a random time-varying delay system is developed that guarantees the designed controller can satisfy the requirements of stability and maneuverability. The desired controller gain is then found based on the linear matrix inequalities. Finally, as a real application, a quarter-vehicle suspension system model is provided to demonstrate the benefits and validity of the proposed control law.

Passivity-Based Robust Sampled-Data Control for Markovian Jump Systems

In this paper, the problem of passivity-based robust sampled-data control is investigated for continuous-time Markovian jump systems (MJSs). First, using parameters-dependent Lyapunov functionals consisting of looped-functionals, stochastic sufficient passivity criteria for continuous-time polytopic uncertain MJSs are proposed. As a corollary, we get the stochastic sufficient passivity criteria for continuous-time nominal MJSs. Based on the obtained stochastic sufficient passivity criteria, time-independent state feedback sampled-data controllers are designed. Then, in order to get a time-dependent state feedback sampled-data controller, parameters-dependent time-scheduled Lyapunov functionals consisting of looped-functionals are developed. New stochastic sufficient passivity criteria are obtained. Furthermore, based on the stochastic sufficient passivity criteria, the time-dependent state feedback sampled-data controllers are designed. Four numerical simulation examples are provided to illustrate the effectiveness of the proposed method.

Sampled-Data Set Stabilization of Impulsive Boolean Networks Based on a Hybrid Index Model

This article investigates the set stabilization of impulsive Boolean control networks (IBCNs) by sampled-data state feedback control based on a hybrid index model. It is worth mentioning that the 2-D index model has the ability to characterize the instantaneousness of ideal impulses and describe complicated impulsive behaviors. To avoid Zeno phenomenon, the judging conditions for forward completeness are derived. Subsequently, an algorithm is designed to obtain the largest sampled point control invariant set (SPCIS) of a given set in the hybrid domain, and its validity is further authenticated. Accordingly, a necessary and sufficient condition is derived for the set stabilization of IBCNs in the hybrid domain, and all time-optimal sampled-data state feedback controllers are designed. The similar results are also obtained for IBCNs in the time domain. Compared with set stabilization in the time domain, set stabilization in the hybrid domain not only focuses on the dynamics at each time instant but also concerns every jumping state. It results in that every SPCIS in the hybrid domain is a subset of a certain SPCIS in the time domain. Eventually, the $\lambda$ switch with impulsive disturbances is modeled as a reduced IBCN, which is presented to demonstrate the obtained results.

Finite-time control of switched systems under asynchronism based on quantized sampled-data

This work makes a discussion on the finite-time control for a class of switched linear systems with average dwell time and asynchronous switching. First, a sufficient finite-time boundedness condition for the closed-loop systems is obtained by choosing suitable mode-dependent and quantization-error-dependent Lyapunov functionals. Further, base on the derived result, the quantized sampled-data state feedback controller is designed to guarantee the finite-time boundedness of the considered systems. At the end, an illustrative example is provided to verify the correctness and effectiveness of the proposed results in this paper.

Sampled-Data State Feedback Control for the Set Stabilization of Boolean Control Networks

This paper studies the set stabilization of Boolean control networks (BCNs) under sampled-data state feedback control (SDSFC). The main research content is divided into two parts. First, the topological structure of BCNs under given SDSFC is investigated. The fixed point and sampled cycle are defined, respectively. It is found that sampled cycles allow elements to be repeated and not every element can be regarded as an initial state, and this is quite different from conventional cycles of BCNs. A theorem is presented to calculate the number of fixed points and an algorithm is given to find all fixed points and sampled cycles. Second, the set stabilization problem of BCNs by SDSFC is investigated based on the sampled point set and the sampled point control invariant set (SPCIS). A necessary and sufficient condition is derived for the global set stabilization of BCNs by SDSFC, and further sampled-data state feedback controllers are also designed. The interesting thing is that if a state enters the SPCIS as an unsampled point, then it may run out of the given set again, which is in sharp contrast to conventional BCNs. Finally, an example is given to illustrate the efficiency of the obtained results.

Sampled-Data Stabilization for Boolean Control Networks With Infinite Stochastic Sampling.

Sampled-data state feedback control with stochastic sampling periods for Boolean control networks (BCNs) is investigated in this article. First, based on the algebraic form of BCNs, stochastic sampled-data state feedback control is applied to stabilize the considered system to a fixed point or a given set. Two kinds of distributions of stochastic sampling periods are considered. First, the distribution of sampling periods is assumed to be independent identically distributed (i.i.d.) in the range of any positive integers and the second distribution of sampling periods is assumed to follow an infinite Markov process. A BCN with infinite stochastic sampling periods proves to be equivalent to a finite stochastic switched system, based on which, necessary and sufficient conditions are given to guarantee the stabilization and set stabilization of the BCN with stochastic sampling periods. For the first one, two algorithms are given to guarantee the stabilization and set stabilization of the considered system. For the second one, necessary and sufficient conditions are all presented in the linear programming form. Examples are listed to show the effectiveness of our results.

On Practical Stability Preservation Under Fast Sampling and Accurate Quantization of Feedbacks for Nonlinear Time-Delay Systems

In this article, we deal with the problem of stabilizing a nonlinear system with state-delays by means of quantized sampled-data state feedback control laws. Quantization in the state measurements and in the input signal are simultaneously considered. Fully nonlinear (i.e., possibly nonaffine in the control) time-delay systems are studied. Sufficient conditions are provided such that suitably fast sampling and accurate quantization of the state feedback at hand yield semiglobal practical stability, with arbitrarily small final target ball of the origin. Nonlinear delay-free systems are addressed as a special case: it is shown that the above sufficient conditions, ensuring the semiglobal practical stability, are satisfied if the continuous-time static state feedback controller is a global stabilizer. The theory of stabilization in the sample-and-hold sense is used. The theoretical results are validated through an example.

When Is a Nonlinear System Semiglobally Asymptotically Stabilizable by Digital Feedback?

For multi-input–multi-output (MIMO) nonlinear systems, we prove that while global asymptotic stabilizability may not ensure semiglobal asymptotic stabilizability (SGAS) by sampled-data state feedback, global asymptotic plus local exponential stabilizability (GALES) does imply the existence of an SGAS sampled-data state feedback controller. Based on this result, we further prove the main contribution of this article: GALES and uniform observability imply SGAS by sampled-data output feedback, which is indeed a hybrid version of the “separation principle” for nonlinear systems. The development of the “digital separation principle” is made possible by employing a subtle Lyapunov argument that makes the estimation of domains of attraction and semiglobal asymptotic analysis relatively intuitive and simple, without involving intricate Lyapunov functions and the corresponding level sets. Results on SGAS by sampled-data feedback for representative classes of nonlinear systems are also given as illustrations.