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An improved prescribed performance control using a backstepping technique and adaptive fuzzy is proposed for a strict feedback nonlinear dynamic system. A new virtual variable was defined to generate the virtual control that forces the tracking errors to fall within prescribed boundaries, and an adaptive fuzzy system was used to obtain required approximation performances. A strict feedback controller and adaptive laws for estimating the unknown non-linear function were designed to avoid a singularity problem and calculation of the explosive number of terms generated by the error transformations of conventional error constraint method and the recursive steps of traditional backstepping control. Lyapunov stability analysis confirmed the boundedness and convergence of the closed-loop system. The prescribed error constraint performance of the proposed control scheme was validated by applying it to control the position of a second-order non-linear system and a robot manipulator.

In this study, a novel online adaptive dynamic programming (ADP)-based algorithm is developed for solving the optimal control problem of affine non-linear continuous-time systems with unknown internal dynamics. The present algorithm employs an observer–critic architecture to approximate the Hamilton–Jacobi–Bellman equation. Two neural networks (NNs) are used in this architecture: an NN state observer is constructed to estimate the unknown system dynamics and a critic NN is designed to derive the optimal control instead of typical action–critic dual networks employed in traditional ADP algorithms. Based on the developed architecture, the observer NN and the critic NN are tuned simultaneously. Meanwhile, unlike existing tuning laws for the critic, the newly developed critic update rule not only ensures convergence of the critic to the optimal control but also guarantees stability of the closed-loop system. No initial stabilising control is required, and by using recorded and instantaneous data simultaneously for the adaptation of the critic, the restrictive persistence of excitation condition is relaxed. In addition, Lyapunov direct method is utilised to demonstrate the uniform ultimate boundedness of the weights of the observer NN and the critic NN. Finally, an example is provided to verify the effectiveness of the present approach.

In this paper, the non-fragile H∞ controller design problem for a class of nonlinear singular Markovian jump systems (SMJSs) with time-varying delay and generally uncertain transition rates is considered. We construct a new Lyapunov-Krasovskii functional (LKF) containing double integral terms, by decomposing the integral interval and introducing the free weight matrices, new sufficient conditions on singular stochastic finite-time boundedness (SSFTB) and singular stochastic H∞ finite-time boundedness (SSH∞FTB) of the closed-loop (C-L) SMJSs are derived. Then, a non-fragile finite-time H∞ controller is designed to ensure the SSH∞FTB of the C-L systems with strict LMIs, although existing the controller gain perturbations. Finally, a numerical example and two practical examples of DC motor model and aircraft propulsion system model are provided to illustrate the effectiveness and feasibility of the method.

In this paper, we developed a cancer dynamical system that incorporates the interaction of tumor cells, immune systems, and drug reaction systems to investigate the impact and therapeutic implications of a fractional order Caputo derivative’s with memory effects. The solutions of the proposed system are shown to be bounded and positive. The existence and uniqueness of the solutions of the suggested model are examined using a few fixed-point theorems. The global stability of the system is examined through the use of Lyapunov’s first derivative functions. For various fractional values, solutions to the fractional order system are obtained with the help of a fractional operator with a power law kernel. The kernel also checks for unique solutions and verification of the scheme through mathematical analysis using novel approaches. Next, a simulation of the derived iterative technique is made for various fractional orders against the real data at different fractional order values. This fractional order model can be used to investigate the dynamics of tumor cells, the interactions between tumor cells and immune cells, and the effects of medications on the disease. The proposed system’s controllability and observability are further addressed by using various therapies as inputs and normal cells as output. A linear control system with a closed-loop design, in which the drug is the input and treated cells are the output, is used to investigate the influence of cancer treatments on different patients.

This paper is concerned with the problems of finite-time boundedness and finite-time H ∞ control for a class of uncertain systems with time-varying delays and exogenous disturbance. By using appropriately chosen Lyapunov-Krasovskii functional (LKF), together with the new integral inequality, new sufficient conditions of finite-time boundedness (FTB) for uncertain time-delay systems are given in terms of linear matrix inequalities (LMIs). Then, by designing the output feedback controller, we established new sufficient conditions to guarantee that the closed-loop system is finite-time bounded with H ∞ performance index. The desired controller gain matrix can be obtained by solving the obtained LMIs. Furthermore, we give a criterion of finite-time stability for the closed-loop system without external disturbance based on the output feedback control. Finally, some numerical examples are given to illustrate the effectiveness of the proposed methods.

This paper mainly investigates the problem of finite-time H ∞ control for a class of uncertain Markovian jump nonlinear systems (MJNSs) with time-varying delay and generally uncertain transition rates. By constructing the appropriate Lyapunov–Krasovskii functional and free weighting matrices, a novel criterion on finite-time boundedness for the MJNSs with H ∞ performance is derived. We use a special way to deal with the bilinear terms, the mode-dependent state feedback controller is designed to ensure the H ∞ finite-time boundedness of the closed-loop system in the forms of strict linear matrix inequalities. Finally, numerical and practical examples are given to demonstrate the effectiveness of the proposed method.

This paper is concerned with asynchronous finite-time H∞ control for a class of discrete-time switched linear systems via admissible edge-dependent average dwell time (AED-ADT) approach. Firstly, by considering the switching time delay between the system and the state feedback controller, appropriate Lyapunov functions are constructed for asynchronous and synchronous switching, respectively. Secondly, for the existence of a set of state feedback controllers, a sufficient condition which guarantees the finite-time boundedness of the closed-loop system with AED-ADT is proposed. Thirdly, a sufficient condition for finite-time H∞ control with a prescribed H∞ performance is further developed based on the obtained result. Finally, a numerical example is given to verify the validity of the proposed theoretical results.

This paper presents a novel distributed robust adaptive control architecture for leader–follower networked multiagent systems with static undirected communication graph topologies to mitigate the effects of time-varying sensor and actuator attacks, and time-invariant plant parameter uncertainty. The proposed adaptive control architecture guarantees uniform ultimate boundedness of the controlled closed-loop system. Two numerical examples are provided to illustrate the efficacy of the proposed distributed robust adaptive control architecture.

This paper addresses the problem of finite-time boundedness (FTB) for a class of Markovian jump systems (MJSs) via sliding mode control (SMC) technique, in which there may happen actuator faults in all of control channels and mismatched external disturbance. By means of the available boundary information of actuator faults, a suitable sliding mode controller is designed such that state trajectories are driven to sliding surface before a specified finite (possibly short) time interval. Furthermore, a partitioning strategy is introduced to derive the sufficient conditions for ensuring the FTB of the closed-loop systems over the whole specified finite-time interval including the reaching phase and the sliding motion phase. Finally, a practical example are provided from an F-404 aircraft engine system to illustrate the proposed method.

The fixed-time congestion control problem of TCP/AQM networks with UDP flows and un-modeled uncertainties has been studied thoroughly in this paper. The fluid-flow based TCP/AQM network system model is analyzed, and a fixed-time adaptive congestion control algorithm is proposed for the nonlinear network system model with unknown UDP flows and un-modeled uncertainty. The new control algorithm was derived using combined requirements for the fixed-time control and the prescribed performance control by employing the back-stepping technique and the fuzzy approximation methodology. The universal approximation property of fuzzy-logic system models is used to deal with the external disturbance and the uncertainty that may appear in the network system. Using the prescribed performance technology, the transient and steady state performances of the tracking error are shown to have been enforced to meet the design requirements. Using the back-stepping methodology, a fixed-time AQM controller is designed so as to ensure that the fixed time of the closed-loop system response remains bounded. The obtained simulation results demonstrate the extent of effectiveness and superiority of the proposed design relative to known previous results.