Sharif Digital Repository

Finding an optimal control strategy for a nonlinear uncertain system is a challenging problem in the area of nonlinear controller design. In this paper, a two-level control algorithm is developed for robust optimal control of large-scale nonlinear systems. For this purpose, using a decomposition/coordination framework, the large-scale nonlinear system is first decomposed into several smaller subsystems, at the first level, where a closed-form solution as a feedback of states and interactions is obtained to optimize each subsystem. At the second level, a substitution-type prediction method, as a coordination strategy, is used to compensate the nonlinear terms of the system and to predict the... 

This paper considers the output feedback adaptive controller design problem for a class of discrete-time nonlinear systems in output feedback form with unknown control directions and preceded by unknown hysteresis. The problem of lacking in a-priori knowledge on the control directions and unknown hysteresis are solved by using the discrete Nussbaum gain and Prandtl-Ishlinskii model, respectively. The system is transformed into the form of a nonlinear auto regressive moving average (NARMA) model to construct an output feedback control. To overcome the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead-zone technique are constructed... 

This paper introduces a new filter for nonlinear systems state estimation. The new filter formulates the state estimation problem as a stochastic dynamic optimization problem and utilizes a new stochastic method based on simplex technique to find and track the best estimation. The vertices of the simplex search the state space dynamically in a similar scheme to the optimization algorithm, known as Nelder-Mead simplex. The parameters of the proposed filter are tuned, using an information visualization technique to identify the optimal region of the parameters space. The visualization is performed using the concept of parallel coordinates. The proposed filter is applied to estimate the state... 

In this paper, a new decomposition-coordination framework is presented for two-level optimal control of large-scale nonlinear systems. In the proposed approach, decomposition is performed by defining an interaction vector, while coordination is based on a new interaction prediction approach. In the first level, sub-problems are solved for nonlinear dynamics using a gradient method, while in the second level, the coordination is done using the gradient of coordination errors. This is in contrast to the conventional gradient-type coordination schemes, where they use the gradient of Lagrangian function. It is shown that the proposed decomposition-coordination framework considerably reduces the... 

There are many physical phenomena in engineering applications that are mostly modeled as stochastic differential equations. Sensor noise and environmental disturbance are two main sources of randomness. Determination of a closed-form analytical solution for the dynamical systems under random excitation is significantly useful for further investigations of these systems. Linear systems with stochastic excitation obey simple classified rules, leading to straightforward procedures for derivation of their analytical solutions. However, it is not the case for nonlinear systems with stochastic excitation, where no comprehensive method has been developed to be applicable to all such systems. This... 

In this paper, We develop concurrent learning adaptive controller, which uses recorded and current data concurrently for adaptation, to model reference adaptive control (MRAC) of uncertain switched nonlinear systems. In standard MRAC architecture for switched systems, the adaptive update laws are derived based on the gradient descent scheme, but here we developed two novel parameter estimation schemes by using modification terms in adaptation laws in which recorded data are used simultaneously with current data and a triggering time is considered in which a sufficient condition on the linear independence of the recorded data is obtained to guarantee the exponential convergence of tracking... 

In this paper, we propose a new derivative-free preconditioned conjugate gradient method in order for solving large-scale square and under-determined nonlinear systems of equations. The proposed method is also equipped with a relaxed nonmonotone line search technique. Under some suitable assumptions, the global convergence property is established. Numerical results on some square and under-determined test systems show the efficiency and effectiveness of the new method in practice. An application of the new method for solving nonlinear integro-differential equations is also provided. © 2016 Elsevier Ltd  

This article presents a robust adaptive fractional order proportional integral derivative controller for a class of uncertain fractional order nonlinear systems using fractional order sliding mode control. The goal is to achieve closed-loop control system robustness against the system uncertainty and external disturbance. The fractional order proportional integral derivative controller gains are adjustable and will be updated using the gradient method from a proper sliding surface. A supervisory controller is used to guarantee the stability of the closed-loop fractional order proportional integral derivative control system. Finally, fractional order Duffing–Holmes system is used to verify... 

This paper is concerned with the stability of nonlinear Lipschitz systems subject to bounded process and measurement noises when transmission from sensor to controller is subject to distortion due to quantization. A stabilizing technique and a sufficient condition relating transmission rate to Lipschitz coefficients are presented for almost sure asymptotic bounded stability of nonlinear uncertain Lipschitz systems. In the absence of process and measurement noises, it is shown that the proposed stabilizing technique results in almost sure asymptotic stability. Computer simulations illustrate the satisfactory performance of the proposed technique for almost sure asymptotic bounded stability... 

In this paper, we propose an optimal control technique for a class of continuous-time nonlinear systems. The key idea of the proposed approach is to parametrize continuous stale trajectories by sequences of a finite number of intermediate target states; namely, waypoint sequences. It is shown that the optimal control problem for transferring the state from one waypoint to the next is given an explicit-form suboptimal solution, by means of linear approximation. Thus the original continuous-time nonlinear control problem reduces to a finite-dimensional optimization problem of waypoint sequences. Any efficient numerical optimization method, such as the interior-reflection Newton method, can be... 

Fuzzy sliding mode control (FSMC) as a robust and intelligent nonlinear control technique is proposed to control processes with severe nonlinearity and unknown models. The performance of the proposed method has been evaluated for both single input single output (SISO) and MIMO nonlinear systems through its application in three severely nonlinear processes that are frequently used as benchmarks of nonlinear process control strategies. The evaluation shows that, despite its lack of dependence on the process model, the proposed method performs almost the same as conventional sliding mode control alternatives that utilize all the information that exists in the mathematical model of the process.... 

This paper proposes event-triggered rules for stabilizing the equilibrium point of a class of nonlinear systems, on the basis of indefinite Lyapunov theory. Unlike the traditional event-triggered control methods, which have been constructed based on the Lyapunov theory, the timederivative of the corresponding Lyapunov function can be positive in some time periods by using the proposed eventtriggered rules. For a class of uncertain nonlinear systems with matched uncertainty, the proposed event-triggered controller guarantees that the trajectories of the system tend to an arbitrary small neighborhood of the equilibrium point of the system. Numerical examples confirm the obtained analytical... 

This paper proposes event-triggered rules for stabilizing the equilibrium point of a class of nonlinear systems, on the basis of indefinite Lyapunov theory. Unlike the traditional event-triggered control methods, which have been constructed based on the Lyapunov theory, the timederivative of the corresponding Lyapunov function can be positive in some time periods by using the proposed eventtriggered rules. For a class of uncertain nonlinear systems with matched uncertainty, the proposed event-triggered controller guarantees that the trajectories of the system tend to an arbitrary small neighborhood of the equilibrium point of the system. Numerical examples confirm the obtained analytical... 

In this paper, a distributed model predictive control is proposed to control Lipschitz nonlinear systems. The cooperative distributed scheme is considered where a global infinite horizon objective function is optimized for each subsystem, exploiting the state and input information of other subsystems. Thus, each control law is obtained separately as a state feedback of all system's states by solving a set of linear matrix inequalities. Due to convexity of the design, convergence properties at each iteration are established. Additionally, the proposed algorithm is modified to optimize only one control input at a time, which leads to a further reduction in the computation load. Finally, two... 

This brief proposes event-Triggered rules for stabilizing the equilibrium point of a class of nonlinear systems, on the basis of indefinite Lyapunov theory. Unlike the traditional event-Triggered control methods, which have been constructed based on the Lyapunov theory, the time-derivative of the corresponding Lyapunov function can be positive in some time periods by using the proposed event-Triggered rules. For a class of uncertain nonlinear systems with matched uncertainty, the proposed event-Triggered controller guarantees that the trajectories of the system tend to an arbitrary small neighborhood of the equilibrium point of the system. Numerical examples confirm the obtained analytical... 

Equivariant adaptive separation via independence (EASI) is one of the most successful algorithms for blind source separation (BSS). However, the user has to choose non-linearities, and usually simple (but non-optimal) cubic polynomials are applied. In this paper, the optimal choice of these non-linearities is addressed. We show that this optimal non-linearity is the output score function difference (SFD). Contrary to simple non-linearities usually used in EASI (such as cubic polynomials), the optimal choice is neither component-wise nor fixed: it is a multivariate function which depends on the output distributions. Finally, we derive three adaptive algorithms for estimating the SFD and... 

In this paper, a mixed event-triggered and continuous-time control method is proposed, which can guarantee finite-time stabilisation of the fixed point in a class of time-varying nonlinear systems. Benefiting from an event-triggered framework, which is constructed based on the indefinite Lyapunov theory, the communication/computation costs in the transient time can be reduced by using the proposed method. In a special case, this method is converted to a fully event-triggered control strategy for asymptotic stabilisation of the fixed point in the considered class of time-varying nonlinear systems. The effectiveness of the proposed method is verified by numerical simulations. © 2021 Informa UK...