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.

Optimal Deterministic State Estimation—A First Step

1984 ◽  
Vol 106 (2) ◽  
pp. 176-178 ◽  
Author(s):  
R. G. Jacquot
Keyword(s):  
Objective Function ◽  
Linear Time ◽  
Estimation Error ◽  
Stochastic Estimation ◽  
Initial Condition ◽  
State Estimator ◽  
First Order ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

Optimal deterministic observers are derived for all first order linear time invariant systems. The optimization process consists of minimizing an objective function which is quadratic in the observer gain and in the estimation error. The objective function was chosen such that the resulting observer gains would be independent of system initial-condition which would, in general, be unknown to the state estimator. The results of this optimization are sensible in the light of the stochastic estimation results of Kalman.

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 Efficient Model Predictive Algorithms for Tracking of Periodic Signals

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yun-Chung Chu ◽  
Michael Z. Q. Chen
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Operating Point ◽  
Quadratic Program ◽  
Efficient Manner ◽  
Linear Time Invariant ◽  
Predictive Algorithms ◽  
Model Predictive Controllers ◽  
Linear Time Invariant Systems ◽  
Time Invariant

This paper studies the design of efficient model predictive controllers for fast-sampling linear time-invariant systems subject to input constraints to track a set of periodic references. The problem is decomposed into a steady-state subproblem that determines the optimal asymptotic operating point and a transient subproblem that drives the given plant to this operating point. While the transient subproblem is a small-sized quadratic program, the steady-state subproblem can easily involve hundreds of variables and constraints. The decomposition allows these two subproblems of very different computational complexities to be solved in parallel with different sampling rates. Moreover, a receding horizon approach is adopted for the steady-state subproblem to spread the optimization over time in an efficient manner, making its solution possible for fast-sampling systems. Besides the conventional formulation based on the control inputs as variables, a parameterization using a dynamic policy on the inputs is introduced, which further reduces the online computational requirements. Both proposed algorithms possess nice convergence properties, which are also verified with computer simulations.

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