Showing papers on "Riccati equation published in 2020"

Developed comparative analysis of metaheuristic optimization algorithms for optimal active control of structures

Abstract: A developed comparative analysis of metaheuristic optimization algorithms has been used for optimal active control of structures. The linear quadratic regulator (LQR) has ignored the external excitation in solving the Riccati equation with no sufficient optimal results. To enhance the efficiency of LQR and overcome the non-optimality problem, six intelligent optimization methods including BAT, BEE, differential evolution, firefly, harmony search and imperialist competitive algorithm have been discretely added to wavelet-based LQR to seek the attained optimum feedback gains. The proposed approach has not required the solution of Riccati equation enabling the excitation effect in controlling process. Employing this advantage by each of six mentioned algorithms to three-story and eight-story structures under different earthquakes led to define (1) the best solution, (2) convergence rate and (3) computational effort of all methods. The purpose of this research is to study the aforementioned methods besides the superiority of ICA in finding the optimal responses for active control problem. Numerical simulations have confirmed that the proposed controller is enabling to significantly reduce the structural responses using less control energy compared to LQR.

Applications of three methods for obtaining optical soliton solutions for the Lakshmanan–Porsezian–Daniel model with Kerr law nonlinearity

Abstract: This paper examines new travelling wave solutions to the Lakshmanan–Porsezian–Daniel (LPD) model with Kerr nonlinearity using Backlund transformation method based on Riccati equation, Kudryashov method and a new auxiliary ordinary differential equation (ODE). The three methods are adequately utilised, and some new rational-type hyperbolic and trigonometric function solutions are derived in different shapes for the aforementioned model. We confirm that our methods are more efficient than the other methods and it might be used in many other such types of nonlinear equations arising in the basic fabric of communications network technology and nonlinear optics.

Team-Optimal Solution of Finite Number of Mean-Field Coupled LQG Subsystems.

Abstract: A decentralized control system with linear dynamics, quadratic cost, and Gaussian disturbances is considered. The system consists of a finite number of subsystems whose dynamics and per-step cost function are coupled through their mean-field (empirical average). The system has mean-field sharing information structure, i.e., each controller observes the state of its local subsystem (either perfectly or with noise) and the mean-field. It is shown that the optimal control law is unique, linear, and identical across all subsystems. Moreover, the optimal gains are computed by solving two decoupled Riccati equations in the full observation model and by solving an additional filter Riccati equation in the noisy observation model. These Riccati equations do not depend on the number of subsystems. It is also shown that the optimal decentralized performance is the same as the optimal centralized performance. An example, motivated by smart grids, is presented to illustrate the result.

Observer-Based Dynamic Event-Triggered Strategies for Leader-Following Consensus of Multi-Agent Systems With Disturbances

Abstract: This paper studies leader-following bounded consensus problem for linear multi-agent systems (MASs) with exogenous disturbances under an observer-based dynamic event-triggered scheme. To guarantee performance requirements, and avoid frequent updates of the sensors, and the controllers at the same time, two independent event-triggered schemes with dynamic threshold are proposed in sensor-to-observer (S-O), and controller-to-actuator (C-A) channels, respectively. And a fully distributed observer event-based controller is designed, which only requires the observer information from neighboring followers, and itself for each follower. With the help of the Riccati equation, and inequality techniques, some simple, and convenient sufficient conditions are derived to ensure that the closed loop system converges to a bounded region exponentially. Moreover, the proposed dynamic event-triggered mechanisms in S-O, and C-A channels do not only lessen the transmission load, and controller update, but also exclude the Zeno behavior. Finally, a numerical example is given to verify the correctness, and efficiency of our results.

Optical solitons of space-time fractional Fokas–Lenells equation with two versatile integration architectures

Abstract: Nonlinear Schrodinger’s equation and its variation structures assume a significant job in soliton dynamics. The soliton solutions of space-time fractional Fokas–Lenells equation with a relatively new definition of local M-derivative have been recovered by utilizing improved $\tan (\frac{\phi (\eta )}{2})$ -expansion method and generalized projective Riccati equation method. The obtained solutions are periodic, dark, bright, singular, rational, along with few forms of combo-soliton solutions. These solutions are given under constraints conditions which ensure their existence. The impact of local fractional parameter is featured by its graphical portrayal. 2D and 3D diagrams are drawn to illustrate the efficacy of the conformable fractional order on the behavior of some of those solutions. The secured solutions of this model have dynamic and significant justifications for some real-world physical occurrences. Our study shows that the suggested schemes are effective, reliable, and simple for solving different types of nonlinear differential equations.

Hybrid Nonlinear Observers for Inertial Navigation Using Landmark Measurements

Abstract: This article considers the problem of attitude, position, and linear velocity estimation for rigid body systems relying on inertial measurement unit and landmark measurements. We propose two hybrid nonlinear observers on the matrix Lie group $\text{SE}_2(3)$ , leading to global exponential stability. The first observer relies on fixed gains, while the second one uses variable gains depending on the solution of a continuous Riccati equation. These observers are then extended to handle biased angular velocity and linear acceleration measurements. Both simulation and experimental results are presented to illustrate the performance of the proposed observers.

H∞ Pinning Control of Complex Dynamical Networks Under Dynamic Quantization Effects: A Coupled Backward Riccati Equation Approach.

Abstract: In this article, a pinning control strategy is developed for the finite-horizon H∞ synchronization problem for a kind of discrete time-varying nonlinear complex dynamical network in a digital communication circumstance. For the sake of complying with the digitized data exchange, a feedback-type dynamic quantizer is introduced to reflect the transformation from the raw signals into the discrete-valued ones. Then, a quantized pinning control scheme takes place on a small fraction of the network nodes with the hope of cutting down the control expenses while achieving the expected global synchronization objective. Subsequently, by resorting to the completing-the-square technique, a sufficient condition is established to ensure the finite-horizon H∞ index of the synchronization error dynamics against both quantization errors and external noises. Moreover, a controller design algorithm is put forward via an auxiliary H₂-type criterion, and the desired controller gains are acquired in terms of two coupled backward Riccati equations. Finally, the validity of the presented results is verified via a simulation example.

Nonlinear Suboptimal Guidance Law With Impact Angle Constraint: An SDRE-Based Approach

Abstract: In this article, a guidance law with impact angle constraint is developed using the state-dependent Riccati equation (SDRE) technique. First, the nonlinear guidance dynamics consisting of line-of-sight (LOS) angle rate and error is formulated under a planar engagement scenario. After the state-dependent coefficient parameterization, a nonlinear regulator problem is formed to concurrently zero LOS angle rate and error. Second, a preliminary guidance law is directly developed under the framework of the SDRE technique. By applying the Lyapunov stability analysis, a nonlinear suboptimal guidance law is obtained through further parameter modifications. Then, the proposed guidance law is extended to attack maneuvering targets. Finally, the effectiveness of the proposed guidance law is demonstrated through numerical simulations.

Finite-Horizon Robust Suboptimal Control-Based Impact Angle Guidance

Abstract: This paper presents impact angle guidance based on finite-horizon robust optimal control. This approach, a fusion of newly proposed finite-time state-dependent Riccati equation and integral sliding-mode-control, solves finite-horizon tracking problem for input-affine nonlinear systems with specified terminal conditions. It also ensures robustness against external disturbances and uncertainties from beginning. The technique for ensuring specified final-time involves deriving closed-form control expression in terms of approximate solution of differential Riccati equation, which further reduces to solutions of algebraic Riccati and Lyapunov equations. This yields computationally efficient algorithm. To alleviate chattering, the supertwisting algorithm is incorporated with the proposed technique. Guidance strategy is derived after converting impact angle problem to tracking one using the proposed algorithm. Efficacy of the proposed guidance is vindicated for various engagement geometries, and also compared with an existing guidance strategy.

Exact Solution of Two-Dimensional Fractional Partial Differential Equations

Abstract: In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati equation. This method is a combination of the Sumudu transform method and decomposition method. The fractional derivative is described in the Caputo sense. The results obtained show that the approach is easy to implement and accurate when applied to various fractional differential equations.

Distance-Based Multiagent Formation Control With Energy Constraints Using SDRE

Abstract: We present an optimal control method for distance-based formation control of multiagent systems with energy constraints. We combine the rigid graph theory and state-dependent Riccati equation method to develop a multiagent formation control scheme. We defined a normalized rigidity matrix and use it for the rigorous stability analysis. The proposed method asymptotically minimizes weighted cost functional that includes formation and energy consumption costs. Furthermore, we propose a solution for the global asymptotic stability and collision avoidance. Simulation results illustrate the effectiveness of the proposed method in two- and three-dimensional spaces.

Backward Stochastic Riccati Equation with Jumps Associated with Stochastic Linear Quadratic Optimal Control with Jumps and Random Coefficients

Abstract: In this paper, we investigate the solvability of matrix valued backward stochastic Riccati equations with jumps (BSREJ), which are associated with a stochastic linear quadratic (SLQ) optimal contro...

Infinite-Horizon Differentiable Model Predictive Control

Abstract: This paper proposes a differentiable linear quadratic Model Predictive Control (MPC) framework for safe imitation learning. The infinite-horizon cost is enforced using a terminal cost function obtained from the discrete-time algebraic Riccati equation (DARE), so that the learned controller can be proven to be stabilizing in closed-loop. A central contribution is the derivation of the analytical derivative of the solution of the DARE, thereby allowing the use of differentiation-based learning methods. A further contribution is the structure of the MPC optimization problem: an augmented Lagrangian method ensures that the MPC optimization is feasible throughout training whilst enforcing hard constraints on state and input, and a pre-stabilizing controller ensures that the MPC solution and derivatives are accurate at each iteration. The learning capabilities of the framework are demonstrated in a set of numerical studies.

SDRE-Based Integral Sliding Mode Control for Wind Energy Conversion Systems

Abstract: This paper proposes a novel integral sliding mode control (ISMC) scheme based on numerically solving a state-dependent Ricatti equation (SDRE), nonlinear feedback control for wind energy conversion systems (WECSs) with permanent magnet synchronous generators (PMSGs). Unlike the conventional ISMC, the proposed control system is designed with nonlinear near optimal feedback control part to take into account nonlinearities of the WECSs. The Taylor series are used to approximate the solutions of SDRE. More specifically, the nonlinear optimal feedback control has been obtained by solving continuous algebraic Ricatti and Lyapunov equations. Sliding variables are designed such that reaching phase is eliminated and stability is guaranteed. The proposed control method equipped with high-order observer can guarantee more superior results than linear techniques such as linear quadratic regulator (LQR), conventional ISMC, and first-order sliding-mode control (SMC) method. Increasing the number of terms of the Taylor’s series of the proposed control law provides better approximation, therefore the performance is improved. However, this increases the computational burden. The effectiveness of the control method is validated via simulations in MATLAB/Simulink under nominal parameters and model uncertainties.

Digital implementation of a continuous-time nonlinear optimal controller: An experimental study with real-time computations.

Abstract: In this paper, the digital implementation of a continuous-time robust nonlinear optimal controller is presented as an experimental study with real-time computations. Complicated computations, solutions, and algorithms of nonlinear optimal policies were always reported as limits to experimental implementations. This work uses a combination of integral sliding mode control (ISMC) and the state-dependent Riccati equation (SDRE) approach for controlling an experimental setup, a rotary inverted pendulum (RIP) with nonlinear dynamics. Designing in the continuous-time domain and performing an experiment using digital computers are common and that leads to extra tuning in practice. Digital components are considered in simulations to provide a more real output and omit extra tuning. Analysis of sampling time effect on instability of a stable controller was done and the obtained bound of sampling time was verified in the experiment. The experimental study showed that the computations of the proposed controller were able to be programmed into the platform interface with time-varying sampling time which was bounded to the generated sampling time in the simulation. Successful swinging up and stabilization of the RIP demonstrated the effectiveness of the ISMC plus SDRE approach. The comparison of the proposed controller with the solo SDRE controller validated the results and showed the performance of the design.

Adaptive non-linear high gain observer based sensorless speed estimation of an induction motor

Abstract: An efficient sensor-less speed estimator, based on an adaptive non-linear high gain observer (HGO) which uses only the measured stator currents and control voltages in the presence of measurement noise, is proposed to estimate the speed of an induction motor. The proposed observer is an improved version of the common HGOs proposed in the literature. The observer gain, involving the use of a scalar time-varying design parameter governed by the Riccati differential equation, guarantees the best compromise between the fast convergence of the states and noise rejection with such adaptation of gains that the internal states of the observer exert low influence during the transient period and thus prevent system peaking. The design methodology of the proposed observer is given and its stability is studied. Results of simulation studies demonstrate that robustness and efficiency of the proposed observer are maintained under critical operating conditions, even where the efficiency of the fixed gain observer is decreased.

State Dependent Riccati Equation (SDRE) controller design for moving obstacle avoidance in mobile robot

Abstract: In this paper, a new navigating method for a non-holonomic wheeled moving robot in a dynamic environment with the moving obstacles is proposed. This method is indeed the combination of the nonlinear optimal controller based on State-Dependent Riccati Equation (SDRE) and an obstacle avoidance algorithm named artificial potential field (APF). The corresponding cost function of the SDRE is obtained of APF algorithm. APF algorithm forces the robot to approach the target as an attracting (low-potential) point and to get away from the obstacle as a repulsing (high-potential) point. This method calculates the best path from origin to destination which also implicitly guaranties the stability. The obtained path is the best according to the both amount of traveled distance and input energy. Moreover, this approach not only avoid both fixed and moving obstacle, but also create a smooth path in presence of them. Keeping the nonlinear structure of the system instead of eliminating them during the linearization process is the advantage of SDRE method. Here, the robot navigation is done in the presence of the three different movements of obstacle: (1) fixed speed, (2) fixed acceleration and (3) non-uniform circular. The represented simulation results indicate a suitable performance of the proposed algorithm.

A variety of new traveling and localized solitary wave solutions of a nonlinear model describing the nonlinear low- pass electrical transmission lines

Abstract: In this work, we focus on investigating the traveling and other localized solitary wave propagation in nonlinear low-pass electrical transmission lines model practicing the new modified sub-ODE method, the unified Riccati equation expansion method, and the fractional linear transform method. A variety of traveling and solitary wave solutions are emerging comprising of bright, dark, kink, anti-kink, hyperbolic function, and doubly periodic Jacobian elliptic function solutions. The applied three integration schemes are reliable and stalwart for acquiring the new kink, bright, dark, periodic and non-singular soliton solutions of the wave propagation in nonlinear low-pass electrical transmission lines. Also, we give the geometric description of some of the obtained solutions for the considered model by computing the most important geometric quantities viz the Gaussian and the mean curvatures. To display the extant physical significance of the considered model equation, some two, three-dimensional figures and density profiles of the acquired solutions are illustrated for the specific choice of arbitrary parameters. The effects of the variation of nonlinear parameters of the nonlinear low-pass electrical transmission lines model on the evolution of soliton solutions are demonstrated. In addition, all derived solutions were verified by substituting back into the considered equation with the aid of Mathematica software. Furthermore, a comparison of our results for the considered model with the obtained solutions in the literature is also provided.

Robust control for vibration control systems with dead-zone band and time delay under severe disturbance using adaptive fuzzy neural network

Abstract: This study proposes a novel adaptive control method to deal with the dead-zone and time delay issues in actuators of vibration control systems. The controller is formulated based on a type-2 fuzzy neural network integrating with a new modification of Riccati-like equation. The developed new type Riccati-like equation is significant as it reduces energy consumption of control inputs to minimum. Two approaches are suggested to improve performance of the system using the basic elements of Riccati equation. In addition, a fuzzy neural network is applied to approximate the unmodeled dynamics and a sliding mode controller is developed to enhance the robustness of the system against uncertainties and disturbances. After proving the stability of the proposed controller via Lyapunov criterion, the effectiveness of the proposed approach is validated based on computer simulation for vibration control of a vehicle seat suspension. It is demonstrated that the unwanted vibrations due to external excitations are well controlled despite of the presence of dead-zone and time delay in actuators. Furthermore, when comparing with other two state-of-the-art robust controllers [ [23] , [33] ], the proposed controller provides better vibration suppression capacity and requires less energy consumption.

Observer-based robust control for flexible-joint robot manipulators: A state-dependent Riccati equation-based approach:

Abstract: In this paper, the robust control problem is tackled by employing the state-dependent Riccati equation (SDRE) for uncertain systems with unmeasurable states subject to mismatched time-varying distu...

Output Consensus of Heterogeneous Multiagent Systems: A Distributed Observer-Based Approach

Abstract: As the control tasks become complex, fulfilling such tasks cooperatively is the first choice in practice In this article, the output consensus problem of heterogeneous multiagent systems is studied by deploying distributed observers in follower agents Each observer in the follower only measures part of the leader's output, which relieves the burden of a simple agent when the leader's output is of large-scale dimensions Then, all followers in the system work cooperatively to estimate the full state of the leader By using parameterized Riccati equation and output regulation theory, sufficient conditions are given to design the distributed observers and the output consensus protocol Finally, a numerical example is conducted to verify the obtained result

On the convergence and stability of fractional singular Kalman filter and Riccati equation

Abstract: In our recent paper [1] , we have developed a simple algorithm for the state estimation of discrete-time linear stochastic fractional-order singular (FOS) systems based on the deterministic least squares method. In this paper, we shall consider the asymptotic properties of the obtained generalized Riccati equation and the associated state estimator. The approach is based on the analysis in detail of the derived filter and algebraic Riccati equation by generalizing significantly the results for standard causal systems, in which provide us conditions for the stability and convergence of the fractional singular Kalman filter (FSKF). Also, conditions under which the Riccati equation has a unique positive semi-definite (PSD) solution are given. Towards this, stability studies of discrete-time FOS state-space systems are investigated, and detectability and stabilizability criterions have been derived. Some examples are performed and verified using numerical simulations in order to illustrate the given analysis.

New Analytical and Numerical Results For Fractional Bogoyavlensky-Konopelchenko Equation Arising in Fluid Dynamics

Abstract: In this article, (2 + 1)-dimensional time fractional Bogoyavlensky-Konopelchenko (BK) equation is studied, which describes the interaction of wave propagating along the x axis and y axis. To acquire the exact solutions of BK equation we employed sub equation method that is predicated on Riccati equation, and for numerical solutions the residual power series method is implemented. Some graphical results that compares the numerical and analytical solutions are given for different values of μ. Also comparative table for the obtained solutions is presented.