Adaptive Inverse Nonlinear Optimal Control Based on Finite-Time Concurrent Learning and Semidefinite Programming.

This article investigates the problem of inverse optimal control (IOC) for a class of nonlinear affine systems. An adaptive IOC approach is proposed to recover the cost functional using only the system state data, which integrates the finite-time concurrent learning (FTCL) technique and the semidefinite programming (SDP) technique. First, an identifier neural network (NN) is employed to approximate the unknown nonlinear control policy, and an FTCL-based update law is proposed to estimate the weights of the identifier NN online, which removes the traditional persistent excitation (PE) condition. Moreover, the finite-time convergence as well as the uniformly ultimately boundness (UUB) of estimation error of the identifier NN weights are analysed according to whether or not there exists the identifier NN approximation error. Then, with the help of a value NN for approximating the value function, an SDP problem with a quadratic objective function can be set up for determining the weighting matrices of the cost functional. Finally, simulation results are presented to validate the proposed method.

Fuzzy Boundary Sampled-Data Control for Nonlinear Parabolic DPSs.

For a nonlinear parabolic distributed parameter system (DPS), a fuzzy boundary sampled-data (SD) control method is introduced in this article, where distributed SD measurement and boundary SD measurement are respected. Initially, this nonlinear parabolic DPS is represented precisely by a Takagi-Sugeno (T-S) fuzzy parabolic partial differential equation (PDE) model. Subsequently, under distributed SD measurement and boundary SD measurement, a fuzzy boundary SD control design is obtained via linear matrix inequalities (LMIs) on the basis of the T-S fuzzy parabolic PDE model to guarantee exponential stability for closed-loop parabolic DPS by using inequality techniques and a LF. Furthermore, respecting the property of membership functions, we present some LMI-based fuzzy boundary SD control design conditions. Finally, the effectiveness of the designed fuzzy boundary SD controller is demonstrated via two simulation examples.

Adaptive event-triggered extended dissipative synchronization of delayed reaction-diffusion neural networks under deception attacks.

Under spatially averaged measurements (SAMs) and deception attacks, this article mainly studies the problem of extended dissipativity output synchronization of delayed reaction-diffusion neural networks via an adaptive event-triggered sampled-data (AETSD) control strategy. Compared with the existing ETSD control methods with constant thresholds, our scheme can be adaptively adjusted according to the current sampling and latest transmitted signals and is realized based on limited sensors and actuators. Firstly, an AETSD control scheme is proposed to save the limited transmission channel. Secondly, some synchronization criteria under SAMs and deception attacks are established by utilizing Lyapunov-Krasovskii functional and inequality techniques. Then, by solving linear matrix inequalities (LMIs), we obtain the desired AETSD controller, which can satisfy the specified level of extended dissipativity behaviors. Lastly, one numerical example is given to demonstrate the validity of the proposed method.

Human-in-the-Loop Behavior Modeling via an Integral Concurrent Adaptive Inverse Reinforcement Learning.

One goal of artificial intelligence (AI) research is to teach machines how to learn from humans, such that they can perform a certain task in a natural human-like way. In this article, an online adaptive inverse reinforcement learning (IRL) approach to human behavior modeling is proposed to enhance machine intelligence for a class of linear human-in-the-loop (HiTL) systems using the state data only, where the human behavior is described by a linear quadratic optimal control model with an unknown weighting matrix for the quadratic cost function. First, an integral concurrent adaptive law is developed to learn the human feedback gain matrix online using the demonstrated state data only, which removes the persistent excitation (PE) conditions required by traditional adaptive estimation approaches and thus is more in line with real applications. Then, with the learned feedback gain matrix, the IRL problem is formulated as a linear matrix inequality (LMI) optimization problem, which can be efficiently solved to retrieve the weighting matrix of the human cost function. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approach.

Learning Human Behavior in Shared Control: Adaptive Inverse Differential Game Approach.

To enhance the collaborative intelligence of a machine, it is important for the machine to understand what behavior a human may adopt to interact with the machine when performing a task in shared control. In this study, an online behavior learning method is proposed for continuous-time linear human-in-the-loop shared control systems by using the system state data only. A two-player nonzero-sum linear quadratic dynamic game paradigm is used for modeling the control interaction between a human operator and an automation that actively compensates for human control action. In this game model, the cost function representing the human behavior is assumed to have an unknown weighting matrix. Here, we want to learn the human behavior or retrieve the weighting matrix by using the system state data only. Accordingly, a new adaptive inverse differential game (IDG) method, which integrates concurrent learning (CL) and linear matrix inequality (LMI) optimization, is proposed. First, a CL-based adaptive law and an interactive controller of the automation are developed to estimate the feedback gain matrix of the human online, and second, an LMI optimization problem is solved to determine the weighting matrix of the human cost function. Finally, simulation results on a cooperative shared control driver assistance system are provided to elucidate the feasibility of the developed method.

Finite-Time Passivity for Coupled Fractional-Order Neural Networks With Multistate or Multiderivative Couplings.

This article mainly delves into the finite-time passivity (FTP) for coupled fractional-order neural networks with multistate couplings (CFNNMSCs) or coupled fractional-order neural networks with multiderivative couplings (CFNNMDCs). Distinguishing from the traditional FTP definitions, several concepts of FTP for fractional-order systems are given. On one hand, we present several sufficient conditions to ensure the FTP for CFNNMSCs by artfully designing a state-feedback controller and an adaptive state-feedback controller. On the other hand, by utilizing some inequality techniques, two sets of FTP criteria for CFNNMDCs are also established on the basis of the state-feedback and adaptive state-feedback controllers. Finally, numerical examples are used to demonstrate the validity of the derived FTP criteria.

Passivity and Finite-Time Passivity for Multi-Weighted Fractional-Order Complex Networks With Fixed and Adaptive Couplings.

This article presents several new α -passivity and α -finite-time passivity ( α -FTP) concepts for the fractional-order systems with different input and output dimensions, which are distinct from the concepts for integer-order systems and extend the existing passivity and FTP definitions to some extent. On one hand, we not only develop some sufficient conditions for ensuring the α -passivity of the multi-weighted fractional-order complex dynamical networks (MWFOCDNs) with fixed and adaptive couplings, but also discuss the synchronization for the MWFOCDNs based on the α -output-strict passivity ( α -OSP). On the other hand, the α -FTP for the MWFOCDNs with fixed and adaptive couplings are also studied on the basis of the designed state feedback controller, and the relationship between finite-time synchronization (FTS) and α -FTP for the MWFOCDNs is also illustrated. Finally, two numerical examples with simulation results are used to demonstrate the validity of the obtained criteria.

Fuzzy Boundary Control for Nonlinear Delayed DPSs Under Boundary Measurements.

For nonlinear delayed distributed parameter systems (DDPSs), this article considers a fuzzy boundary control (FBC) under boundary measurements (BMs). Initially, we accurately describe the nonlinear DDPS through a Takagi-Sugeno (T-S) fuzzy partial differential-difference equation (PDDE). Then, in accordance with the T-S fuzzy PDDE model, an FBC design under BMs ensuring the exponential stability for closed-loop DDPS is subsequently presented by spatial linear matrix inequalities (SLMIs) via using Wirtinger's inequality, Halanay's inequality, and the Lyapunov direct method, which respects the fast-varying and slow-varying delays. Moreover, we formulate SLMIs as LMIs for solving the fuzzy boundary controller design of nonlinear DDPSs under BMs. Finally, the effectiveness of the proposed FBC strategy is presented via simulation examples.

Pinning Spatiotemporal Sampled-Data Synchronization of Coupled Reaction-Diffusion Neural Networks Under Deception Attacks.

In this article, we investigate the pinning spatiotemporal sampled-data (SD) synchronization of coupled reaction-diffusion neural networks (CRDNNs), which are directed networks with SD in time and space communications under random deception attacks. In order to handle with the random deception attacks, we establish a directed CRDNN model, which respects the impacts of variable sampling and random deception attacks within a unified framework. Through the designed pinning spatiotemporal SD controller, sufficient conditions are obtained by linear matrix inequalities (LMIs) that guarantee the mean square exponential stability of the synchronization error system (SES) derived by utilizing inequality techniques, the stochastic analysis technique, and Lyapunov-Krasovskii functional (LKF). Finally, a numerical example is utilized to support the presented pinning spatiotemporal SD synchronization method.

Finite-Time Passivity and Synchronization of Multi-Weighted Complex Dynamical Networks Under PD Control.

This article focuses on finite-time passivity (FTP) and finite-time synchronization (FTS) for complex dynamical networks with multiple state/derivative couplings based on the proportional-derivative (PD) control method. Several criteria of FTP for complex dynamical networks with multiple state couplings (CDNMSCs) are formulated by utilizing the PD controller and constructing an appropriate Lyapunov function. Furthermore, FTP is further used to investigate the FTS in CDNMSCs under the PD controller. In addition, the FTP and FTS for complex dynamical networks with multiple derivative couplings (CDNMDCs) are also studied by exploiting the PD control method and some inequality techniques. Finally, two numerical examples are worked out to demonstrate the validity of the presented PD controllers.

Distributed Cooperative Quantum Learning for Discrete-Time Multiagent Source Exploration With Information Prompts.

In light of optimization theory and swarm evolutionary schemes, under multiple single-integrator mobile agents equipped with sensors and prompters, this article addresses a discrete-time multiagent source exploration problem with information prompts. Regarding information prompts as constraints on the unknown target, by virtue of penalty function skills (PFSs) and sequential unconstrained minimization techniques (SUMTs), the agents are driven toward the source under the guidance of the control strategy. In two cases of available and unavailable gradient information, a quantum potential well, an average optimal position estimator (AOPE), and a global optimal position estimator (GOPE) are introduced into swarm evolutionary schemes with a periodically oscillating weight, such that distributed cooperative quantum learning (DCQL) policy is proposed as a control strategy under communication restrictions, where AOPE and GOPE are developed relying on distributed consensus theory. In particular, when the gradient is unavailable, we put forth an adaptive generalized Bernstein neural network (AGBNN) to replace it based on excellent properties of Bernstein polynomials and adaptive approaches. Further, a performance analysis for the proposed policy is executed on the convergence and computational complexity, which ensures the accuracy and efficiency of the source exploration in theory. Ultimately, a simulation test is carried out, and the results validate the practicability and effectiveness of the offered method.

Fuzzy Control Design of Nonlinear Time-Delay Parabolic PDE Systems Under Mobile Collocated Actuators and Sensors.

Via mobile sensing measurements, this study applies the Takagi-Sugeno (T-S) fuzzy model to deal with the mobile fuzzy control design problem for nonlinear time-delay parabolic partial differential equation (PDE) systems. Initially, we use a T-S fuzzy model to accurately represent the nonlinear time-delay parabolic PDE system. Subsequently, under the assumption that the actuators and sensors are collocated while the spatial domain is divided by several subdomains, a control scheme containing the fuzzy controllers and the guidance of mobile actuator/sensor pairs is proposed based on the obtained T-S fuzzy model, where the projection modification guidance to be designed can guarantee that each mobile actuator/sensor pair moves within the prescribed area. Then, using the Lyapunov direct method and integral inequalities, a membership-function-dependent design of fuzzy controllers plus mobile actuator/sensor guidance laws is developed to render the resulting closed-loop time-delay system exponentially stable. Moreover, the exponential decay rate can also be increased by the proposed mobile guidance laws. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed design method and the application of mobile actuator/sensor pairs contributes to accelerating the convergence speed of the closed-loop state.

Design of Fuzzy State Observer and Mobile Sensor Guidance for Semilinear Parabolic PDE Systems.

This article investigates the issue of the fuzzy observer design for the semilinear parabolic partial differential equation (PDE) systems with mobile sensing measurements. Initially, we employ a Takagi-Sugeno (T-S) fuzzy PDE model to represent the semilinear parabolic PDE system accurately in a local region. Afterward, via the T-S fuzzy model and under the hypothesis that the spatial domain is divided by several subdomains in the light of the number of sensors, a state observation scheme which contains a fuzzy observer and the mobile sensor guidance is proposed. Then, by means of the Lyapunov direct method and integral inequalities, a design method of the fuzzy observer and mobile sensor guidance is provided to render the resulting state estimation error system exponentially stable, while the designed mobile sensor guidance can increase the exponential decay rate. Finally, numerical simulations are presented to show that the proposed fuzzy observer design approach is effective and the employment of mobile sensors contributes to improving the response speed of the state estimation error in comparison with the static ones.

Synthesis With Guaranteed Cost and Less Human Intervention for Human-in-the-Loop Control Systems.

This article studies the problem of synthesis with guaranteed cost and less human intervention for linear human-in-the-loop (HiTL) control systems. Initially, the human behaviors are modeled via a hidden controlled Markov process, which not only considers the inference's stochasticity and observation's uncertainty of the human internal state but also takes the control input to human into account. Then, to integrate both models of human and machine as well as their interaction, a hidden controlled Markov jump system (HCMJS) is constructed. With the aid of the stochastic Lyapunov functional together with the bilinear matrix inequality technique, a sufficient condition for the existence of human-assistance controllers is derived on the basis of the HCMJS model, which not only guarantees the stochastic stability of the closed-loop HiTL system but also provides a prescribed upper bound for the quadratic cost function. Moreover, to achieve less human intervention while meeting the desired cost level, an algorithm that mixes the particle swarm optimization and linear matrix inequality technique is proposed to seek a suitable feedback control law to the human and a human-assistance control law to the machine. Finally, the proposed method is applied to a driver-assistance system to verify its effectiveness.

Design of Suboptimal Local Piecewise Fuzzy Controller With Multiple Constraints for Quasi-Linear Spatiotemporal Dynamic Systems.

This paper discusses the problem of suboptimal local piecewise H ∞ fuzzy control of quasi-linear spatiotemporal dynamic systems with control magnitude constraints. A Takagi-Sugeno fuzzy partial differential equation (PDE) model with space-varying coefficient matrices is first assumed to be derived for exactly describing nonlinear system dynamics. In the light of the fuzzy model, a local piecewise fuzzy feedback controller is then constructed to guarantee the exponential stability with a prescribed H ∞ disturbance attenuation level for the resulting closed-loop system, while the control constraints are also ensured. A sufficient condition on the existence of such fuzzy controller is developed by the Lyapunov direct method and an integral inequality and presented in terms of space algebraic linear matrix inequalities (LMIs) coupled with LMIs. By virtue of extreme value theorem, a suboptimal-constrained local piecewise H ∞ fuzzy control design in the sense of minimizing the disturbance attenuation level is formulated as a minimization optimization problem with LMI constraints. Finally, the proposed method is applied to solve the feedback control of a quasi-linear FitzHugh-Nagumo equation with space-varying coefficients, and simulation results show its effectiveness and merit.

Finite-Time Output Synchronization and H∞ Output Synchronization of Coupled Neural Networks With Multiple Output Couplings.

This article investigates the finite-time output synchronization and H∞ output synchronization problems for coupled neural networks with multiple output couplings (CNNMOC), respectively. By choosing appropriate state feedback controllers, several finite-time output synchronization and H∞ output synchronization criteria are proposed for the CNNMOC. Moreover, a coupling-weight adjustment scheme is also developed to guarantee the finite-time output synchronization and H∞ output synchronization of CNNMOC. Finally, two numerical examples are given to verify the effectiveness of the presented criteria.

Quantized Sampled-Data Synchronization of Delayed Reaction-Diffusion Neural Networks Under Spatially Point Measurements.

This article considers the synchronization problem of delayed reaction-diffusion neural networks via quantized sampled-data (SD) control under spatially point measurements (SPMs), where distributed and discrete delays are considered. The synchronization scheme, which takes into account the communication limitations of quantization and variable sampling, is based on SPMs and only available in a finite number of fixed spatial points. By utilizing inequality techniques and Lyapunov-Krasovskii functional, some synchronization criteria via a quantized SD controller under SPMs are established and presented by linear matrix inequalities, which can ensure the exponential stability of the synchronization error system containing the drive and response dynamics. Finally, two numerical examples are offered to support the proposed quantized SD synchronization method.

Finite-Time Passivity and Synchronization of Complex Dynamical Networks With State and Derivative Coupling.

In this article, two kinds of complex dynamical networks (CDNs) with state and derivative coupling are investigated, respectively. First, some important concepts about finite-time passivity (FTP), finite-time output strict passivity, and finite-time input strict passivity are introduced. By making use of state-feedback controllers and adaptive state-feedback controllers, several sufficient conditions are given to guarantee the FTP of these two network models. On the other hand, based on the obtained FTP results, some finite-time synchronization criteria for the CDNs with state and derivative coupling are gained. Finally, two simulation examples are proposed to verify the availability of the derived results.

Output Synchronization of Complex Dynamical Networks With Multiple Output or Output Derivative Couplings.

In this paper, the output synchronization problem for complex dynamical networks (CDNs) with multiple output or output derivative couplings is discussed in detail. Under the help of Lyapunov functional and inequality techniques, an output synchronization criterion is presented for CDNs with multiple output couplings (CDNMOCs). To ensure the output synchronization of CDNMOCs, an adaptive control scheme is also devised. Similarly, we also take into account the adaptive output synchronization and output synchronization of CDNs with multiple output derivative couplings. At last, several numerical examples are designed to testify the effectiveness of the proposed results.

Fuzzy Control Under Spatially Local Averaged Measurements for Nonlinear Distributed Parameter Systems With Time-Varying Delay.

This paper introduces a fuzzy control (FC) under spatially local averaged measurements (SLAMs) for nonlinear-delayed distributed parameter systems (DDPSs) represented by parabolic partial differential-difference equations (PDdEs), where the fast-varying time delay and slow-varying one are considered. A Takagi-Sugeno (T-S) fuzzy PDdE model is first derived to exactly describe the nonlinear DDPSs. Then, by virtue of the T-S fuzzy PDdE model and a Lyapunov-Krasovskii functional, an FC design under SLAMs, where the membership functions of the proposed FC law are determined by the measurement output and independent of the fuzzy PDdE plant model, is developed on basis of spatial linear matrix inequalities (SLMIs) to guarantee the exponential stability for the resulting closed-loop DDPSs. Lastly, a numerical example is offered to support the presented approach.