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In this paper, a novel covariance tracking receding horizon (CTRH) process is proposed to design a robust control algorithm. Some drawbacks of the equivalent robust algorithms, including infeasibility, computational complexity, and non-optimality, are alleviated in this process. Hence, first, covariance analysis is applied to rephrase the dynamic equation of the system to model the structural uncertainties. Afterward, this approach is extended to the future time horizons as the discrete-time formulations are to be embedded in the receding horizon controller framework. Then, a new constrained quadratic programming cost function is proposed considering the covariance matrix to mitigate the trajectory dispersion along with the control action. The final control rule is estimated by solving the new cost function using the Hildreth method. The efficiency of the developed robust algorithm is demonstrated by numerical simulation of two benchmark buildings equipped with active tendon systems subjected to earthquake excitations. The competency of the proposed method (CTRH) is then proven using nominal and various perturbed scenarios and outputs compared to the linear–quadratic–Gaussian (LQG) controller, sliding mode control (SMC), H∞, and conventional receding horizon (CRH) controllers, and comparative results are presented. The outcomes indicate that the proposed method not only well reduces the controlled responses compared to uncontrolled one but also demonstrate a high level of robustness against various other control approaches. Less computational complexity due to not adding any linear matrix inequalities and constraints is also one of the prominent features of the proposed approach. [ABSTRACT FROM AUTHOR]

The robust algorithm is proposed for parametric and structurally uncertain linear plants under external bounded disturbances. The structural uncertainty is an unknown dynamic order of the model of plants. The developed algorithm provides plant output tracking for a smooth bounded reference signal with a required accuracy at a finite time. It is assumed that only scalar input and output of the plants are available for measurement, but not their derivatives. For the synthesis of the control algorithm we use a modified backstepping algorithm. The synthesis of control algorithm is separated into rsteps, where ris an upper bound of the relative degree of control plant model. At each step we synthesize auxiliary controls that stabilize each subsystem about a zero. At the last step we synthesize a basic control law, which provides output tracking for smooth reference signal. It is shown that for the implementation of the algorithm we need to use only one filter of the control signal and the simplified control laws obtained by application of the real derivative elements. It allows simplifying significantly the calculation and implementation of the control system. Numerical examples and results of computer simulation are given, illustrating the operation of the proposed scheme.

The wide real life applications of circular plates under dynamic loading such as laminate saw blades and accurate slitting narrow industrial cutters require special attention to smart structural design that optimally handles the dynamic behavior of these configurations. The purpose of this paper is to investigate the vibration regulation of a sandwich circular plate using a non-fragile robust control strategy. A new dynamic modeling of the piezolaminated structure is proposed based on satisfying the Maxwell static electricity equation and on assuring the full coupling effects of the piezoelectric layers on the host structure. The Eigen functions are chosen optimally such that the boundary conditions for the piezoelectric sensor/actuator are satisfied without additional complexities. In order to reach to the desired performance in vibration attenuation, a robust controller is designed by considering the uncertainties that exist in the system matrices and controller itself. The proposed controller is obtained by solving a system of linear matrix inequalities (LMIs) that are based on the Bounded Real Lemma (BRL). Simulations show that the controller is capable of suppressing the vibration in existence of both the structured uncertainty in the system matrices and the feedback controller gain. [ABSTRACT FROM AUTHOR]

This study examines the issues of robust passivity, feedback passification and global stabilisation for a class of switched non‐linear system with structural uncertainty. First, a sufficient condition for such a system to be robust passive is given by the design of a state‐dependent switching law. Second, a state‐dependent switching law and state feedback controllers are designed to render the resulting closed‐loop system robust passive. Finally, a recursive feedback passification design technique is developed to achieve the global stabilisation problem when the subsystems have any uniform vector relative degree. A numerical example is presented to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this study, a consensus algorithm for multiple non‐linear Euler–Lagrange systems is presented. This controller guarantees that all agents can reach a common state in the workspace. External disturbances acting on the system are included in the closed‐loop stability analysis, and the input‐to‐state properties of the proposed controller are investigated based on the concept of input‐to‐state consensus. Moreover, the influence of structural uncertainty is further discussed on the basis of passivity theory. The robustness of the proposed consensus algorithm is then demonstrated in the presence of both external disturbances and structural uncertainty. Experiments are conducted to validate the effectiveness of the proposed consensus algorithm. [ABSTRACT FROM AUTHOR]

Based on robust control Lyapunov functions (RCLF), an equivalent condition for a function to be an RCLF is given and then a sufficient condition for the robust stabilization, robust practical stabilization and robust asymptotical stabilization is deduced. In addition, the continuous state feedback control law about the pointwise minimum norm is designed to globally asymptotically stabilize the equilibrium of the closed -- loop system. The simulation result shows the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Using coprime fractional techniques and H ∞ -norms, the performance sensitivity of linear systems with five types of simultaneous structural uncertainty is analyzed. Sufficient conditions for the robust stability are derived. Also, the perturbed upper bounds for the sensitivity function matrix and the closed-loop transfer function matrix are presented. [ABSTRACT FROM AUTHOR]

Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state space where such a tipping point might exist. We illustrate how a Bayesian non-parametric approach using a Gaussian process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a stochastic dynamic programming framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favours models without tipping points, leading to harvest policies that guarantee extinction. The Gaussian process dynamic programming (GPDP) performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, as it does not underestimate the uncertainty outside of the observed data. [ABSTRACT FROM AUTHOR]