Decentralized Adaptive Secure Control of Uncertain Nonlinear Time-Varying Interconnected Systems Against Sensor and Actuator Attacks.

In this article, the decentralized adaptive secure control problem for cyber-physical systems (CPSs) against deception attacks is investigated. The CPSs are formed as a type of nonlinear interconnected strict-feedback systems with uncertain time-varying parameters. The attack affects the information transmission between sensor and actuator in a multiplicative manner. A novel decentralized adaptive backstepping secure control strategy is established by exploiting a particular kind of Nussbaum functions and a flat-zone Lyapunov function analysis approach. It is shown that all of closed-loop signals remain globally bounded, and each output signal eventually converges into a small neighborhood of the origin. Simulation results on an illustrative example are provided to display the effectiveness of the proposed control scheme.

Multiple Observer Adaptive Fusion for Uncertainty Estimation and Its Application to Wheel Velocity Systems.

Uncertainty estimation in real-world scenarios is challenged by complexities arising from peaking phenomena and measurement noises. This article introduces a novel scheme for practical uncertainty estimation to mitigate peaking dynamics and enhance overall dynamic behavior. A fusion estimation framework for lumped uncertainties using multiple extended state observers (ESOs) is constructed, and the low-frequency adaptive parameter learning technique is employed to approximate the optimal fusion. The adaptive fusion estimation not only attenuates transient peaks in uncertainty estimation but also attains fast convergence and high accuracy under the high-gain scheduling of ESOs. Furthermore, the robustness of uncertainty estimation against measurement noises is enhanced by cascading filters in the proposed adaptive fusion framework for multiple ESOs. Extensive theoretical analyses are executed to verify practical applicability in peak and noise rejection. Finally, simulations and experiments on the wheel velocity system of a mobile robot are conducted to test the validity and feasibility.

Sliding Mode Fuzzy Control of Stochastic Nonlinear Systems Under Cyber-Attacks.

In this article, the problem of integral sliding mode control (ISMC) for a class of nonlinear systems with stochastic characteristics under cyber-attack is investigated. The control system and the cyber-attack are modeled as an Itô-type stochastic differential equation. The stochastic nonlinear systems are approached by the Takagi-Sugeno fuzzy model. A dynamic ISMC scheme is applied and the states and control input are analyzed within a universal dynamic model. It is demonstrated that trajectory of the system can be confined to the integral sliding surface within finite time, and the stability of closed-loop system under cyber-attack will be guaranteed by using a set of linear matrix inequalities. Following a standard procedure of universal fuzzy ISMC, it is shown that all signals in the closed-loop system will be guaranteed bounded, and the states are asymptotic stochastic stable if some conditions are met. An inverted pendulum is applied to show the effectiveness of our control scheme.

Fast and Smooth Composite Local Learning-Based Adaptive Control.

Model structure representation and fast estimation of perturbations are two key research aspects in adaptive control. This work proposes a composite local learning adaptive control framework, which possesses fast and flexible approximation to system uncertainties and meanwhile smoothens control inputs. Local learning, which is a nonparametric regression approach, is able to automatically adjust the structure of approximator based on data distribution from the local region, but it is sensitive to the outliers and measurement noises. To tackle this problem, the regression filter technique is employed to attenuate the adverse effect of noises by smoothing the output response and state features. In addition, the stable integral adaptation is integrated into local learning framework to further enhance the system robustness and smoothness of the estimation. Through the online elimination of uncertainties, the nominal control performance is recovered when the plant encounters violent perturbations. Stability analysis and numerical simulations are performed to demonstrate the effectiveness and benefits of the proposed control method. The proposed approach exhibits a promising performance in terms of rapid perturbation elimination and accurate tracking control.

Asymptotic adaptive output feedback event-triggered control of uncertain strict-feedback nonlinear systems with sensors triggering.

In this paper, event-triggered output feedback control of a class of high-order nonlinear strict-feedback systems with parametric uncertainties is investigated, in which both of the controller and the parameter estimator are triggered based on a set of event-triggered conditions. Firstly a new one-step control design framework is proposed for the strict-feedback nonlinear systems, therefore both expressions of the controller and the parameter estimate laws are much more simple than those of the recursive design approaches such as backstepping control. Secondly observers are designed to estimate the unknown states, and a set of event-triggering mechanism is proposed for the sensors such that the states are transmitted through the communication network only at the triggering points. The estimated parameter is obtained without real-time integration due to the event-triggered estimator. It is proved that our proposed control law guarantees the closed-loop system is globally bounded and the system output converges to zero asymptotically. It is also proved that the Zeno behavior is excluded. Simulation results demonstrate the effectiveness of the proposed control scheme.

Optimal Control of Temporal Networks With Variable Input and Node-Source Connection.

Many networked systems built upon real-life physical or social interactions have time-varying connections among individual units, where the temporal changes in connectivity and/or interaction strength lead to complicated dynamics. The temporal network model was proposed in the form of controlled linear dynamical systems acting in an ordered sequence of time intervals. One of the core challenges in network science is the control of networks and the optimization of the control strategy. However, most canonical frameworks for solving optimal control problems were established for static networks featuring constant topology. New theories and techniques are yet to be developed for the temporal networks, with an important case being that the input and the source-node connection are both variables. In this work, by formulating a quadratic energy cost without solving the Riccati differential equation, we show that the control effort can be reduced substantially by improving either the system trajectories or the input matrices. The two approaches are further combined in a coordinate descent framework, integrating linearly constrained quadratic programming, and a projected gradient descent method. Taken together, the results underline the potential of temporal networks as energy-efficient control systems and present strategies to improve the control input. Moreover, the proposed algorithms can serve as a starting point for future engineering of real-world temporal networks.

Adaptive Iterative Learning Control of Multiple Autonomous Vehicles With a Time-Varying Reference Under Actuator Faults.

In this article, a distributed adaptive iterative learning control for a group of uncertain autonomous vehicles with a time-varying reference is presented, where the autonomous vehicles are underactuated with parametric uncertainties, the actuators are subject to faults, and the control gains are not fully known. A time-varying reference is adopted, the assumption that the trajectory of the leader is linearly parameterized with some known functions is relaxed, and the control inputs are smooth. To design distributed control scheme for each vehicle, a local compensatory variable is generated based on information collected from its neighbors. The composite energy function is used in stability analysis. It is shown that uniform convergence of consensus errors is guaranteed. An illustrative example is given to demonstrate the effectiveness of the proposed control scheme.

Target Controllability in Multilayer Networks via Minimum-Cost Maximum-Flow Method.

In this article, to maximize the dimension of controllable subspace, we consider target controllability problem with maximum covered nodes set in multiplex networks. We call such an issue as maximum-cost target controllability problem. Likewise, minimum-cost target controllability problem is also introduced which is to find minimum covered node set and driver node set. To address these two issues, we first transform them into a minimum-cost maximum-flow problem based on graph theory. Then an algorithm named target minimum-cost maximum-flow (TMM) is proposed. It is shown that the proposed TMM ensures the target nodes in multiplex networks to be controlled with the minimum number of inputs as well as the maximum (minimum) number of covered nodes. Simulation results on Erdos-Rényi (ER-ER) networks, scale-free (SF-SF) networks, and real-life networks illustrate satisfactory performance of the TMM.

Distributed Adaptive Control for Asymptotically Consensus Tracking of Uncertain Nonlinear Systems With Intermittent Actuator Faults and Directed Communication Topology.

In this article, we investigate the output consensus tracking problem for a class of high-order nonlinear systems with unknown parameters, uncertain external disturbances, and intermittent actuator faults. Under the directed topology conditions, a novel distributed adaptive controller is proposed. The common time-varying trajectory is allowed to be totally unknown by part of subsystems. Therefore, the assumption on the linearly parameterized trajectory signal in most literature is no longer needed. To achieve the relaxation, extra distributed parameter estimators are introduced in all subsystems. Besides, to handle the actuator faults occurring at possibly infinite times, a new adaptive compensation technique is adopted. It is shown that with the proposed scheme, all closed-loop signals are globally uniformly bounded and asymptotically output consensus tracking can be achieved.

Adaptive control of a class of strict feedback nonlinear systems under replay attacks.

The adaptive control of a class of strict-feedback nonlinear system under replay attack is investigated in this paper. Durations of each attack and the resting time after each attack are analyzed and their explicit bounds are presented to ensure closed-loop stability. Two scenarios are considered. In the first scenario, it is shown that if the duration of each attack is less than a given constant, asymptotical convergence of system output is still preserved. The second scenario shows that if the resting time of each attack meets certain condition after each arbitrarily long duration of attack, closed-loop boundedness is still preserved. This shows that the system controlled under our proposed adaptive controller will not be broken down even in the presence of replay attacks. Simulation results are given to illustrate the effectiveness of the control schemes.

Event-triggered adaptive control of a class of nonlinear systems.

In this paper, the event-triggered adaptive control for a class of nonlinear systems in Brunovsky form is considered. The sensors are event-triggered thus the states are transmitted only at the discrete triggering points, which are more efficient in using communication bandwidth. To solve this problem, we design a set of event-triggered conditions and based on which the controller and parameter estimator are designed without the ISS assumption. It is shown that the proposed control schemes guarantee that all the closed-loop signals are semi-globally bounded and the stabilization error converges to the origin asymptotically. The Zeno behavior is also excluded. Simulation results illustrate the effectiveness of our scheme.

Minimum Cost Control of Directed Networks With Selectable Control Inputs.

The minimum cost control problem is one of the most important issues in controlling complex networks. Different from the previous works, in this paper, we consider the minimum cost control problem with selectable inputs by adopting the cost function summed over both quadratic terms of system input and system state with a weighting factor. To address such an issue, the orthonormal-constraint-based projected gradient method is proposed to determine the input matrix iteratively. Convergence of the proposed algorithm is established. Extensive simulation results are carried out to show the effectiveness of the proposed algorithm. We also investigate what kinds of nodes are most important for minimizing average control cost in directed stems/circles and small networks through simulation studies. The presented results in this paper bring meaningful physical insights in controlling the directed networks from an energy point of view.

Fully Distributed Adaptive Consensus Control of a Class of High-Order Nonlinear Systems With a Directed Topology and Unknown Control Directions.

In this paper, we investigate the adaptive consensus control for a class of high-order nonlinear systems with different unknown control directions where communications among the agents are represented by a directed graph. Based on backstepping technique, a fully distributed adaptive control approach is proposed without using global information of the topology. Meanwhile, a novel Nussbaum-type function is proposed to address the consensus control with unknown control directions. It is proved that boundedness of all closed-loop signals and asymptotically consensus tracking for all the agents' outputs are ensured. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme.

L0 norm constraint based external control source allocation for the minimum cost control of directed networks.

Locating a pre-given number of key nodes that are connected to external control sources so as to minimize the cost of controlling a directed network x(t)=Ax(t)+Bu(t), known as the minimum cost control problem, is of critical importance. Considering a network consisting of N nodes with M external control sources, the state of art techniques employ iterative searching to determine the input matrix B that characterizes how nodes are connected to external control sources, in a matrix space RN×M. The nodes having M largest values of a defined importance index are selected as key nodes. However, such techniques may suffer from large performance penalty in some networks due to the diversity of real-life networks. To address this outstanding issue, we propose an iterative method, termed "L0-norm constraint based projected gradient method" (LPGM). We probabilistically search the input matrix in each iteration by restricting its L0 norm as a fixed value M, which implies that each control source is always only connected to a single key node during the whole searching process. Simulation results show that the solution always efficiently approaches a suboptimal key node set in a few iterations. These results provide a new point of view regarding the key nodes selection in the minimum cost control of directed networks.

Decentralized adaptive control of interconnected nonlinear systems with unknown control directions.

In this paper, we propose a decentralized adaptive control scheme for a class of interconnected strict-feedback nonlinear systems without a priori knowledge of subsystems' control directions. To address this problem, a novel Nussbaum-type function is proposed and a key theorem is drawn which involves quantifying the interconnections of multiple Nussbaum-type functions of the subsystems with different control directions in a single inequality. Global stability of the closed-loop system and asymptotic stabilization of subsystems' output are proved and a simulation example is given to illustrate the effectiveness of the proposed control scheme.

Distributed adaptive asymptotically consensus tracking control of uncertain Euler-Lagrange systems under directed graph condition.

In this paper, a backstepping based distributed adaptive control scheme is proposed for multiple uncertain Euler-Lagrange systems under directed graph condition. The common desired trajectory is allowed totally unknown by part of the subsystems and the linearly parameterized trajectory model assumed in currently available results is no longer needed. To compensate the effects due to unknown trajectory information, a smooth function of consensus errors and certain positive integrable functions are introduced in designing virtual control inputs. Besides, to overcome the difficulty of completely counteracting the coupling terms of distributed consensus errors and parameter estimation errors in the presence of asymmetric Laplacian matrix, extra information transmission of local parameter estimates are introduced among linked subsystem and adaptive gain technique is adopted to generate distributed torque inputs. It is shown that with the proposed distributed adaptive control scheme, global uniform boundedness of all the closed-loop signals and asymptotically output consensus tracking can be achieved.

System Identification in Presence of Outliers.

The outlier detection problem for dynamic systems is formulated as a matrix decomposition problem with low rank and sparse matrices, and further recast as a semidefinite programming problem. A fast algorithm is presented to solve the resulting problem while keeping the solution matrix structure and it can greatly reduce the computational cost over the standard interior-point method. The computational burden is further reduced by proper construction of subsets of the raw data without violating low-rank property of the involved matrix. The proposed method can make exact detection of outliers in case of no or little noise in output observations. In case of significant noise, a novel approach based on under-sampling with averaging is developed to denoise while retaining the saliency of outliers, and so-filtered data enables successful outlier detection with the proposed method while the existing filtering methods fail. Use of recovered "clean" data from the proposed method can give much better parameter estimation compared with that based on the raw data.