Zeno-free adaptive event-triggered control design

2018 ◽  
Vol 41 (8) ◽  
pp. 2328-2337 ◽  
Author(s):  
Hassan Adloo ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Degrees Of Freedom ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Performance Criterion ◽  
Linear Time Invariant ◽  
Event Triggering ◽  
Linear Time Invariant Systems ◽  
System States ◽  
Time Invariant ◽  
Event Triggered

This paper presents a new general framework for adaptive event-triggered control strategy to extend average inter-event interval, while maintaining the performance of the system. The proposed event-triggering mechanism is acquired from input to state stability conditions, which is defined in terms of system states as well as an adaptation parameter. Under the Lipschitz assumption, a positive lower bound on sampling durations is also established that is essential to restrain the Zeno behavior. Applying the proposed method to linear time-invariant systems, leads to sufficient conditions to guarantee asymptotic stability in the form of matrix inequalities. Moreover, it is shown that there exist more degrees of freedom to improve the performance criterion from theoretical aspects. Finally, in order to show capability of the proposed method and its better performance compared with some recent works, numerical simulations are presented.

scholarly journals Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 136
Author(s):  
Manuel Duarte-Mermoud ◽  
Javier Gallegos ◽  
Norelys Aguila-Camacho ◽  
Rafael Castro-Linares
Keyword(s):  
Fractional Order ◽  
Performance Optimization ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Minimal Realization ◽  
Linear Time Invariant ◽  
Mixed Order ◽  
Linear Time Invariant Systems ◽  
Minimal Realizations ◽  
Time Invariant

Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers.

Novel Gaussian State Estimator based on H2 Norm and Steady-State Variance

2020 ◽  
Author(s):  
Alesi Augusto De Paula ◽  
Víctor Costa da Silva Campos ◽  
Guilherme Vianna Raffo ◽  
Bruno Otávio Soares Teixeira
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Estimation Error ◽  
Performance Criterion ◽  
Gaussian State ◽  
State Estimator ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Linear Time Invariant System ◽  
Time Invariant

This paper proposes a novel state estimator for discrete-time linear systems with Gaussian noise. The proposed algorithm is a fixed-gain filter, whose observer structure is more general than Kalman one for linear time-invariant systems. Therefore, the steady-state variance of the estimation error is minimized. For white noise stochastic processes, this performance criterion is reduced to the square H2 norm of a given linear time-invariant system. Then, the proposed algorithm is called observer H2 filter (OH2F). This is the standard Wiener-Hopf or Kalman-Bucy filtering problem. As the Kalman predictor and Kalman filter are well-known solutions for such a problem, they are revisited.

Inverse-Dynamics Based State and Disturbance Observers for Linear Time-Invariant Systems

2002 ◽  
Vol 124 (3) ◽  
pp. 375-381 ◽  
Author(s):  
Chia-Shang Liu ◽  
Huei Peng
Keyword(s):  
Inverse Dynamics ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Ground Vehicle ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Disturbance Model ◽  
Rank Conditions ◽  
Time Invariant

An output-feedback observer is proposed in this paper to simultaneously estimate unknown states and disturbances of linear time invariant systems. The states are estimated using a Luenberger-like observer while the disturbance signals are estimated based on an inverse-dynamics motivated algorithm. The proposed schemes can be applied to a wide variety of disturbances since no disturbance model is required in the estimation. Depending on the input/output rank conditions of the plant, two different designs are proposed. The observer gains are selected based on sufficient conditions for exponentially converging estimation. The design procedure is illustrated step-by-step by using two examples: a hypothetical problem and the ground vehicle lateral speed estimation problem. A standard H∞-filter is used as the benchmark to illustrate the performance of the proposed method.

DISSIPATIVE DYNAMICAL SYSTEMS IN A BEHAVIORAL CONTEXT

1991 ◽  
Vol 01 (01) ◽  
pp. 1-25 ◽  
Author(s):  
SIEP WEILAND ◽  
JAN C. WILLEMS
Keyword(s):  
Dynamical Systems ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Dissipative System ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Dissipative Dynamical Systems ◽  
Necessary And Sufficient ◽  
Lq Theory ◽  
Time Invariant

Various conceptual definitions of dissipativeness of time invariant dynamical systems are introduced. A formal distinction is made between external and internal dissipativeness and it is shown that, under certain conditions, these notions are equivalent. A characterization of the class of internal storage functions associated with a dissipative system is given. The results are applied to the class of finite-dimensional linear time invariant systems. Necessary and sufficient conditions for dissipativeness of systems in this class are derived and the relation to LQ-theory is discussed.

scholarly journals Sign-Consensus of Linear Multiagent Systems under a State Observer Protocol

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Wei-Lu Diao ◽  
Cui-Qin Ma
Keyword(s):  
Linear Time ◽  
Sufficient Conditions ◽  
State Observer ◽  
Matrix Analysis ◽  
Positive Sign ◽  
Consensus Protocol ◽  
Linear Time Invariant ◽  
Signed Digraph ◽  
Linear Time Invariant Systems ◽  
Time Invariant

The sign-consensus problem for linear time-invariant systems under signed digraph is considered. The information of the agents’ states is reconstructed, and then, a state observer-type sign-consensus protocol is proposed, whose performance is analyzed using matrix analysis and ordinary differential equation theory. Sufficient conditions for ensuring sign-consensus are given. It is proven that if the adjacency matrix of the signed digraph has strong Perron–Frobenius property or is eventually positive, sign-consensus can be achieved under the proposed protocol. In particular, conventional consensus is a special case of sign-consensus under mild conditions.

scholarly journals Simultaneous exact model matching with stability by output feedback

2017 ◽  
Vol 68 (2) ◽  
pp. 148-152
Author(s):  
Konstadinos H. Kiritsis
Keyword(s):  
Output Feedback ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Dynamic Output Feedback ◽  
Model Matching ◽  
Linear Time Invariant ◽  
Exact Model ◽  
Linear Time Invariant Systems ◽  
Necessary And Sufficient ◽  
Time Invariant

Abstract In this paper, is studied the problem of simultaneous exact model matching by dynamic output feedback for square and invertible linear time invariant systems. In particular, explicit necessary and sufficient conditions are established which guarantee the solvability of the problem with stability and a procedure is given for the computation of dynamic controller which solves the problem.

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