Identified Markov Parameters Research Articles

Markov parameters identification and adaptive iterative learning control for linear discrete-time MIMO systems with higher-order relative degree

For a kind of linear discrete-time-invariant multi-input-multi-output systems with a higher-order relative degree that repetitively operates within a finite time length, the paper exploits a Markov parameters identification method by making use of the multi-operation inputs and outputs obeying a criterion. Simultaneously, an adaptive iterative learning control scheme is architected by formulating the compensator with the sequentially identified Markov parameters and the tracking error in minimizing a performance index consisting of the quadratic tracking error of the next iteration and the compensation cost. Algebraic manipulations including the singular value decomposition of a matrix and the eigenvalues estimation conduct that the identification error of the Markov parameters is monotonically declining as the iteration goes on and a smaller identification ratio in the criterion delivers a faster decline rate. Meanwhile, a rigorous derivation achieves that under the assumption that the initial identification error is within an appropriate range the tracking error is monotonously convergent for the case when the relative degree is unit whilst the tracking error is asymptotically bounded for a positive level for the case where the relative degree is higher. Numerical simulations illustrate the validity and efficiency.

Torsional control of asymmetric buildings using online 3‐D damage detection and adaptive stiffness devices

Developing a smart civil structure, in which the structure instantaneously identifies damages during vibration and makes decisions to compensate or reduce them, is one of the new issues in the seismic control of structures. One of the most important challenges in asymmetric buildings is the torsion due to the damage occurrence in the structure during severe excitation. The aim of this study is to try to reduce the torsional effects and dynamic responses of the structure by combining two strategies, including real time structural health monitoring (SHM) and semi-active control. Hence, a new damage detection method based on identified Markov parameters of the system is proposed to identify the damage in 3-D shear model structures. Also, in order to create a smart structure, a new controller is designed to regulate mechanical characteristics of the installed adaptive stiffness devices based on the detected damages and eccentricity variations in the structure. The performance of the proposed controller and damage detection method is investigated through numerical examples under the influence of various earthquake records. The obtained results reveal that the proposed method estimates the location, amount, and type of damages with acceptable accuracy even with noise contamination of the measured data. Moreover, the presented controller can effectively reduce the increase in the torsional response of the structure owing to the damage occurrence during strong ground motions.

Fault Estimation Filter Design With Guaranteed Stability Using Markov Parameters

For additive actuator and sensor faults, we propose a systematic method to design a state-space fault estimation filter directly from Markov parameters identified from fault-free data. We address this problem by parameterizing a system-inversion-based fault estimation filter with the identified Markov parameters. Even without building an explicit state-space plant model, our novel approach still allows the filter gain design for stabilization and suboptimal $\mathcal{H}_2$ performance. This design freedom cannot be achieved by other existing data-driven fault estimation filter designs so far. Another benefit of our proposed design is the convenience of determining the state order: a higher state order of the filter leads to better estimation performance, at the cost of heavier computational burden. In contrast, order determination is cumbersome when using an identified state-space plant model for the filter design, because of the complicated propagation of the model mismatch into the fault estimation errors. Simulations using an unstable aircraft system illustrate the effectiveness of the proposed new method.

Data-driven robust receding horizon fault estimation

This paper presents a data-driven receding horizon fault estimation method for additive actuator and sensor faults in unknown linear time-invariant systems, with enhanced robustness to stochastic identification errors. State-of-the-art methods construct fault estimators with identified state-space models or Markov parameters, without compensating for identification errors. Motivated by this limitation, we first propose a receding horizon fault estimator parameterized by predictor Markov parameters. This estimator provides (asymptotically) unbiased fault estimates as long as the subsystem from faults to outputs has no unstable transmission zeros. When the identified Markov parameters are used to construct the above fault estimator, stochastic identification errors appear as model uncertainty multiplied with unknown fault signals and online system inputs/outputs (I/O). Based on this fault estimation error analysis, we formulate a mixed-norm problem for the offline robust design that regards online I/O data as unknown. An alternative online mixed-norm problem is also proposed that can further reduce estimation errors at the cost of increased computational burden. Based on a geometrical interpretation of the two proposed mixed-norm problems, systematic methods to tune the user-defined parameters therein are given to achieve desired performance trade-offs. Simulation examples illustrate the benefits of our proposed methods compared to recent literature.

Data-driven sensor fault estimation filter design with guaranteed stability

We propose a systematic method to directly identify a sensor fault estimation filter from plant input/output data collected under fault-free condition. This problem is challenging, especially when skipping the step of building an explicit state-space plant model in data-driven design, because the inverse of the underlying plant dynamics is required and needs to be stable. We show that it is possible to address this problem by relying on a system-inversion-based fault estimation filter that is parameterized using identified Markov parameters. Our novel data-driven approach improves estimation performance by avoiding the propagation of model reduction errors originating from identification of the state-space plant model into the designed filter. Furthermore, it allows additional design freedom to stabilize the obtained filter under the same stabilizability condition as the existing model-based system inversion. This crucial property enables its application to sensor faults in unstable plants, where existing data-driven filter designs could not be applied so far due to the lack of such stability guarantees (even after stabilizing the closed-loop system). A numerical simulation example of sensor faults in an unstable aircraft system illustrates the effectiveness of the proposed new method.

Cautious [formula omitted] optimal control using uncertain Markov parameters identified in closed loop

In this paper, we present a new cautious H 2 optimal design approach based on the noisy and biased Markov parameters identified from a finite number of input and output samples in a closed-loop plant. This approach not only links closed-loop subspace identification with optimal control; but also directly evaluates parametric uncertainties on the identified Markov parameters. Neither a state-space model nor its stochastic uncertainty has to be realized. The effects of the parametric uncertainties on the output predictor and a quadratic cost function are explicitly analyzed. An H 2 optimal control problem is formulated as a “ min max ” problem of the expectation of the cost function with respect to the stochastic noise in the identified parameters. Analytic solution to this problem is derived in a closed form, which avoids computing the empirical mean of the quadratic cost as required by randomized algorithms. An extension of the cautious design to the solution associated with an arbitrary probability is also proposed. The solutions hence lead to easily implementable control laws, robust to the uncertainties in the identified Markov parameters from a closed-loop plant.

Estimation of Markov parameters and time-delay/interactor matrix

The ARMarkov-least squares method is extended to multivariable systems. This method explicitly determines the Markov parameters (impulse response coefficients) of a process using process input–output data and a standard least-squares algorithm. The parameter estimates are consistent and have tighter confidence bounds than those produced by other linear regression methods. The Interactor matrix, which defines the time delays in multivariable systems, can be directly estimated from the Markov parameters. From simulation results it is observed that the Markov parameters estimated by the ARMarkov-LS method are the closest to the actual Markov parameters irrespective of the system order and lead to a better estimate of the interactor matrix than other linear regression methods such as Correlation Analysis, ARX, FIR, etc. The identified Markov parameters and/or the time-delay/interactor matrix can be used directly in the design of model predictive controllers and control loop performance assessment.