Low-Complexity Tracking Control of Unknown Strict-Feedback Systems With Quantitative Performance Guarantees.

This article is concerned with the prescribed performance tracking control problem for the strict-feedback systems with unknown nonlinearities and unmatched disturbances. The challenge lies in the realization of a complete performance specification for trajectory tracking in the sense of quantitatively regulating the peak value, overshoot, settling time, and accuracy while ensuring that the initial condition holds naturally. To this end, an error transformation, equipped with a shifting function, is introduced and incorporated with a new-type barrier function. Then, a class of performance functions is exploited to quantify the settling times and steady-state bounds of the intermediate errors. Moreover, to improve the flexibility of formulating performance specifications for the tracking error, a pair of asymmetric performance boundaries are further designed. With their combination, a novel robust prescribed performance control (PPC) approach is proposed in this article. It not only achieves the quantitative performance guarantees but also preserves the unique simplicity of PPC, evading the needs for function approximation, parameter identification, disturbance estimation, derivative calculation, or command filtering. The above theoretical findings are confirmed via three simulation studies.

Adaptive fuzzy prescribed time tracking control for nonlinear systems with input saturation.

This article investigates the adaptive fuzzy prescribed time tracking control problem for a class of strict-feedback systems simultaneously considering the user-defined asymmetric tracking performance, input saturation, and external disturbances. From the perspective of ensuring the reliability for control implementation, a saturation-based fixed-time funnel boundary is constructed by embedding the modification signals related to input saturation errors into a funnel function, which is capable of automatically enlarging or recovering itself when input saturation occurs or disappears, thereby reducing the risk of system singularity. Subsequently, by constructing a fixed-time tracking performance function, any known bounded tracking error is recast into a new variable with a zero initial value. With such a treatment, funnel boundaries are no longer redeveloped for different initial tracking errors, and meanwhile the behavior of the tracking error is pre-specified as needed over a finite time interval. Also, auxiliary systems are devised to generate the aforesaid modification signals, while compensating for the adverse impact resulting from input saturation. Remarkably, by feat of the backstepping design based on the fuzzy approximation, it is proven that the tracking error converges to a user-defined region within a prescribed time (known as the practically prescribed time tracking), which is achieved without the fractional power feedback of system states. Finally, two simulation examples are presented to confirm the feasibility and effectiveness of the developed approach.

Multiple bottleneck topology TCP/AQM switching network congestion control with input saturation and prescribed performance.

This paper studies the congestion control problem of multiple bottleneck networks. First, this paper regards the routing nodes of the network as multi-agents, and considers its own dynamic process. For the first time, the time-varying characteristics of the number of sessions in the network transmission process and the mutual influence between nodes are considered into the model, and a queue utilization rate switching model is established to describe the dynamics of a single agent. Then, considering the boundedness of the control input, combined with the prescribed performance technique, two congestion controllers are designed by using the backstepping method according to whether the controller depends on the number of sessions. The designed congestion controllers improve the robustness of the TCP/AQM network system in the case of frequent and time-varying sessions in multiple bottleneck networks. In addition, the designed controllers can stabilize different routing nodes of multiple bottleneck networks under different queue lengths, thereby improving the utilization efficiency of the network. Finally, the effectiveness and superiority of the designed controllers are verified by simulation.

Adaptive Finite-Time Command Filtered Controller Design for Nonlinear Systems With Output Constraints and Input Nonlinearities.

This work addresses a finite-time tracking control issue for a class of nonlinear systems with asymmetric time-varying output constraints and input nonlinearities. To guarantee the finite-time convergence of tracking errors, a novel finite-time command filtered backstepping approach is presented by using the command filtered backstepping technique, finite-time theory, and barrier Lyapunov functions. The newly proposed method can not only reduce the complexity of computation of the conventional backstepping control and compensate filtered errors caused by dynamic surface control but also can ensure that the output variables are restricted in compact bounding sets. Moreover, the proposed controller is applied to robot manipulator systems, which guarantees the practical boundedness of all the signals in the closed-loop system. Finally, the effectiveness and practicability of the developed control strategy are validated by a simulation example.

Direct Adaptive Preassigned Finite-Time Control With Time-Delay and Quantized Input Using Neural Network.

This paper investigates an adaptive finite-time control (FTC) problem for a class of strict-feedback nonlinear systems with both time-delays and quantized input from a new point of view. First, a new concept, called preassigned finite-time performance function (PFTF), is defined. Then, another novel notion, called practically preassigned finite-time stability (PPFTS), is introduced. With PFTF and PPFTS in hand, a novel sufficient condition of the FTC is given by using the neural network (NN) control and direct adaptive backstepping technique, which is different from the existing results. In addition, a modified barrier function is first introduced in this work. Moreover, this work is first to focus on the FTC for the situation that the time-delay and quantized input simultaneously exist in the nonlinear systems. Finally, simulation results are carried out to illustrate the effectiveness of the proposed scheme.

Design of adaptive H∞ controller for power system based on prescribed performance.

The design problem of the adaptive robust prescribed performance controller with external disturbance is studied for the excitation system of single-machine infinite power system in here. By combining the H∞theory and adaptive control method, the designed controller not only ensures that the external interference influence on the system is attenuated to a degree of giving, but also the unknown parameter existed in the system can also be estimated. The transient performance of the generator rotor angle can be set in advance with the help of the prescribed performance control (PPC) strategy. Finally, the simulation experiment considers two kinds of faults, namely mechanical fault and short circuit fault, and proves the feasibility and effectiveness via simulation results.

Adaptive fuzzy funnel congestion control for TCP/AQM network.

In this paper, a performance constraint control problem is considered for Transmission Control Protocol/Active Queue Management (TCP/AQM) network with external disturbance and input saturation. On the basis of backstepping-like design procedure and fuzzy approximation technique, an adaptive fuzzy controller with prescribed constraint is achieved to ensure that the transient and steady state performances of the tracking errors can be satisfied. The stability analysis proves that all the signals in the closed-loop system are semi-globally, uniformly and ultimately bounded. The simulation results clarify the feasibility and effectiveness of the proposed approach.

Design of adaptive backstepping congestion controller for TCP networks with UDP flows based on minimax.

The congestion control problem of TCP network systems with user datagram protocol (UDP) flows is investigated in this paper. A nonlinear TCP network model with strict-feedback structure is first established. The unknown UDP flow is regarded as the external disturbance, and the maximum UDP flow is calculated by using the minimax approach. And then, a congestion control algorithm is proposed by using the adaptive backstepping approach. Meanwhile, the adaptive law is employed to estimate the unknown link capacity. The design of the adaptive law is to introduce a parameter mapping mechanism to limit the parameter identification range to a specified interval, thereby improving the estimation efficiency of the parameters. Furthermore, a state-feedback congestion controller is presented to make sure that the output of the system tracks the desired queue. The simulation results show the superiority and feasibility of the proposed method.

Congestion tracking control for uncertain TCP/AQM network based on integral backstepping.

An H∞ congestion tracking control problem for nonlinear transmission control protocol/active queue management (TCP/AQM) network is proposed in this paper. Inspired by the existing network models, a modified TCP/AQM network model with external disturbance and modelling uncertainty is first introduced. And then, a novel function for the desired queue length is defined for the first time, which can simulate the changes in the queue length during a day. Next, a novel AQM scheme is presented to control network congestion by combining H∞ theory and integral backstepping technique. The proposed method guarantees that the better tracking performance of the queue is achieved, and all the signals are asymptotically stable in the closed-loop system in probability. Finally, the effectiveness of the presented algorithm is tested by simulation results.

Adaptive backstepping H∞ tracking control with prescribed performance for internet congestion.

This paper extends the well-known control method, prescribed performance control (PPC), to network congestion control problems. An adaptive H∞ tracking problem for Transmission Control Protocol/Active Queue Management (TCP/AQM) system with external disturbance is studied. Firstly, a modified network model is given. And then, the model is changed to an equivalent error model by using error transformation. Next, to solve the network congestion problem, prescribed performance, backstepping technique, adaptive control and H∞ control are combined to design a congestion controller. Due to the use of prescribed performance, the controller can guarantee both the transient and steady state performance of the system. Meanwhile, the output of the system can track the desired queue, and unknown link capacity can be estimated. Finally, a simulation result is shown to clarify the feasibility and effectiveness of proposed approach.