Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a bounded set. Conditions for the existence and characterization of trapping regions have been established in prior work for boundedness analysis. However, prior solutions have used non-convex optimization methods, resulting in conservative estimates. In this paper, we build on this prior work and provide a convex semidefinite programming condition for the existence of a trapping region. The condition allows for precise verification or falsification of the existence of a trapping region. If a trapping region exists, then we provide a second semidefinite program to compute the least conservative radius of the spherical trapping region. Two low-dimensional systems are provided as examples to illustrate the results. A third high-dimensional example is also included to demonstrate that the computation required for the analysis can be scaled to systems of up to states. The proposed method provides a precise and computationally efficient numerical approach for computing trapping regions. We anticipate this work will benefit future studies on modeling and control of lossless quadratic dynamical systems.
In this paper, a novel robust estimation-based non-fragile controller is designed for a specific class of discrete-time, time-varying, non-linear systems whose non-linear term satisfies the incremental quadratic inequality, which is parameterized by a set of multiplier matrices and sector-bounded conditions. The system is subject to unknown external input with fluctuating controller gain. The proposed approach introduces an improved standard linear filter structure, including non-linear terms and a modified state feedback controller. The stability of the closed-loop system is guaranteed in the framework of linear matrix inequalities (LMIs), and the state estimator and controller gains are determined simultaneously such that the boundedness of the control input is ensured. Moreover, an LMI-based optimization problem is presented to obtain the closed-loop system's maximum domain of attraction (DOA). The benchmark system of RTAC is employed to verify the performance of the proposed control approach.
The precision of the strip thickness is an index of significance in the tandem cold rolling process which makes a difference to the strip quality. However, it is hard to build an accurate mathematical model for thickness control in the tandem cold rolling process, because there exist coupling relationships of complexity between the adjacent stands and unmeasurable process parameters. To overcome the difficulties, a distributed nonlinear model predictive control (DNMPC) strategy with a deep learning method is put forward in this paper, where the auto-regressive radial basis function neural networks are established to model the tandem cold rolling process. For each stand, not only the control input and exit thickness output data of this stand, but also the data of the neighbor stands are selected as the input of the neural network. Besides, the design of the distributed nonlinear model predictive controller turns into an optimization problem, and the gradient method is applied to solve it, which gets rid of the leaning upon mathematical models. Moreover, the stability of the developed method is proven, which indicates the boundedness of the tracking error. The simulations are carried out on three-stand and five-stand examples, and the results verify the efficacy of the proposed DNMPC strategy.
This article focuses on the design of a secure memory-based adaptive event-triggered filter for networked systems subject to hybrid cyber attacks and input limitations. First, a hybrid attack model incorporating denial-of-service (DoS) attacks, deception attacks, and replay attacks is established for filter design. Second, a novel memory-based adaptive event-triggered strategy sensitive to cyber attacks is introduced into the filter design to save network resources, optimize network channel utilization, and prevent network congestion. Subsequently, a novel event-triggered filtering error model is established under hybrid cyber attacks and input limitations. Utilizing Lyapunov–Krasovskii functionals and linear matrix inequality (LMI) techniques, sufficient conditions can be concluded to prove the exponential mean-square stability of the filtering error model with a given performance index. Finally, the effectiveness and the practicality of the obtained conclusions are demonstrated by a numerical simulation and tunnel diode circuit.
This paper explores the issue of prescribed-time optimal formation synchronous tracking control of nonlinear unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) systems. Based on a novel constructed second-order nonlinear UAV-UGV swarm case, the reinforcement learning (RL) method is introduced to obtain the optimal control scheme, and a gradient descent method with a simple positive function for the Hamilton-Jacobi-Bellman (HJB) equation is improved to establish the adaptive actor and critic networks and solve the iterate adaptive laws, which allows adaptive parameters to be trained more thoroughly. Integrating the prescribed-time constraints of formation tasks, the incorporation of traditional prescribed-time functions can result in structural modifications within the RL framework and state coupling, thereby increasing the complexity of control strategy design. Hence, the prescribed-time functions are designed in the critic and actor networks, which address the state coupling and optimize the acquisition of adaptive parameters under the gradient descent method. Then, by employing the aforementioned methods, an optimal synchronous control scheme is proposed to address nonlinear UAV-UGV time-varying formation tracking at a settling time, and a pivotal scaling technique is used for formation stability analysis. Finally, simulation and experiment results are carried out to demonstrate the efficacy of the proposed approach.
Steering a nonlinear system from an initial state to a desired one is a common task in control. While a nominal trajectory can be obtained rather systematically using a model, for example, via numerical optimization, heuristics, or reinforcement learning, the design of a computationally fast and reliable feedback control law that guarantees bounded deviations around the found trajectory can be much more involved. An approach that does not require high online computational power and is well-accepted in industry is gain-scheduling. The results presented here pertain to the boundedness guarantees and the set of safe initial conditions of gain-scheduled control laws, based on subsequent linearizations along the reference trajectory. The approach bounds the uncertainty arising from the linearization process, builds polytopic sets of linear time-varying systems covering the nonlinear dynamics along the trajectory, and exploits sufficient conditions for the existence of a robust polyquadratic Lyapunov function to attempt the derivation of the desired gain-scheduled controller via the solution of linear matrix inequalities (LMIs). A result to estimate an ellipsoidal set of safe initial conditions is provided too. Moreover, arbitrary scheduling strategies between the control gains are considered in the analysis, and the method can also be used to check/assess the boundedness properties obtained with an existing gain-scheduled law. The approach is demonstrated experimentally on a small quadcopter, as well as in simulation to design a scheduled controller for a chemical reactor model and to validate an existing control law for a gantry crane model.
This investigation primarily centers on the reachable-set-based bumpless transfer control (BTC) for the synchronization of switched neutral-type neural networks (SNNNs). In order to mitigate the conservatism inherent in the traditional state-dependent switching strategies (SDSSs) and combined switching strategies (CSSs), an improved CSS leveraging the historical information of neuron states and neutral delay is developed. By constructing a time-dependent multiple Lyapunov-Krasovskii functional (TDMLF) technique, a less conservative criterion for reachable set estimation (RSE) is first established. In the subsequent, the established design framework is further employed by the BTC for the synchronization of SNNNs. The corresponding synchronization criterion is derived, which ensures that the resultant synchronization error influenced by bounded external inputs can be confined to an anticipated bounded set. Also, the underlying control bumps at switching instants during switching instants are effectively constrained to a specific level. Ultimately, the practicability and superiority of the proposed design framework are confirmed via two simulation examples.
This paper proposes a novel integrated guidance and control (IGC) scheme for a bank-to-turn (BTT) hypersonic vehicle (HV) in the dive phase with multi-constraints, input saturation, and complex uncertainties. In the guidance loop, the presence of the terminal impact angle constraints may cause severe saturation of the attack angle, which may lead to the failure of the mission. Motivated by this issue, a range-varying sliding mode surface is constructed, of which the core is a novel line-of-sight (LOS) angle error shaping strategy that drives the LOS angle errors to converge along the prescribed performance functions. On this basis, a range-based prescribed performance function is designed to portray a practical saturation-alleviation convergence characteristic of the LOS angle errors. In the control loop, the barrier Lyapunov function (BLF) and barrier function (BF)-based adaptive law are incorporated to restrict the states within proper regions in the presence of uncertainties. Additionally, an auxiliary system is constructed to deal with the adverse affect caused by input saturation. The stability of the closed-loop system is proved by the Lyapunov stability theory. Finally, the effectiveness and robustness of the proposed IGC scheme are verified through numerical simulations.
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