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In this paper, the robust digital stabilization problem of nonlinear systems is investigated. In particular, a methodology for the design of robust quantized sampled-data stabilizers updated via an event-triggered mechanism is provided for time-varying control-affine nonlinear systems affected by actuation disturbances and measurement noises. The notion of time-varying steepest descent feedback (TSDF), continuous or not, and the Input-to-State Stability (ISS) redesign methodology are used for the development of the proposed robust event-based digital controller. Under the assumption that the actuation disturbances and measurement noises are bounded with a-priori known bounds and that the amplitude of the measurement noises satisfies a certain condition related to the new added robustification term, the following result is proved: there exist a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified TSDF controllers, updated through a proposed event-triggered mechanism, ensures semi-global practical stability of the related closed-loop system regardless of the above uncertainties. In the methodology here proposed, time-varying sampling periods and the non-uniform quantization of the input/output channels are allowed. Moreover, the theory here developed includes the analysis of the intersampling system behaviour. Possible discontinuities in the function describing the TSDF at hand are also managed. The provided results are validated through a numerical example.

This paper proposes a cooperative pursuit strategy against a maneuvering target by introducing a cascaded optimization framework for assignment and guidance. The cooperative guidance algorithm, guaranteeing both encirclement and simultaneous attack constraints, is derived by optimizing the normal impact–direction and tangential impact–time control efforts, respectively. Then, by minimizing the performance index identical to the guidance loop, an assignment approach is proposed to allocate the desired impact direction and time for each pursuer. Since the assignment and guidance strategies share a unified optimization tenet in a cascaded manner, the proposed integrated cooperative method proves more efficient than the existing guidance-only methods. Theoretical analysis and numerical simulations are provided to demonstrate its advantages in synergy efficiency.

This paper investigates the problem of resilient distributed state estimation for a linear system in multi-hop communication networks. First, we introduce a graph-theoretic property, called multiple-hop strong robustness, to formalize the notion of communication and measurement redundancy in multi-hop communication networks. Second, we propose multi-hop communication-based resilient distributed state estimation strategies in the synchronous network and the asynchronous network with time delays, respectively. We provide necessary and sufficient conditions on the network topologies under which the regular agents can still asymptotically estimate the state vector of the system despite the existence of adversarial agents using the property of multiple-hop strong robustness. In contrast to the 1-hop communication-based strategies in the existing results, the proposed multi-hop communication-based strategies can reduce the communication redundancy requirement on the network and accelerate convergence. Finally, we present two examples to verify the effectiveness of the proposed strategies.

This paper revisits classical work of Rauch et al. (1965) and develops a novel statistical method for maximum likelihood (ML) recursive state estimation in general state–space models. The new method is based on statistical estimation theory for incomplete information, which has been well developed primarily for ML parameter estimation (Dempster et al., 1977). Distributional identities for the posterior score function and information matrix of state are established. Using these identities, a fast convergent EM-gradient algorithm is proposed, extending the Lange (1995) algorithm for ML recursive state estimation. It revisits and provides an improvement to the EM-algorithm of Ramadan and Bitmead (2022). An explicit form of the information matrix is developed to provide empirical estimates of the standard errors. Sequential Monte Carlo method is used for the valuation of the score function, information and posterior covariance matrices. Some numerical examples are discussed to exemplify the main results.

We present a novel $Q$-learning algorithm tailored to solve distributionally robust Markov decision problems where the corresponding ambiguity set of transition probabilities for the underlying Markov decision process is a Wasserstein ball around a (possibly estimated) reference measure. We prove convergence of the presented algorithm and provide several examples also using real data to illustrate both the tractability of our algorithm as well as the benefits of considering distributional robustness when solving stochastic optimal control problems, in particular when the estimated distributions turn out to be misspecified in practice.

In this paper, the boundary control problem for a class of flexible riser control systems with input quantization and boundary position constraints is studied. Since quantization errors can adversely affect the performance of the control system, input quantization is an unavoidable issue for maintaining the high accuracy of the system. Partial differential equations are utilized to model the dynamics of the flexible riser system. Based on the partial differential equation model, a new auxiliary term is introduced to compensate for the effects of quantization, and a boundary controller is constructed using the barrier Lyapunov function, which guarantees the stability of the considered system. Moreover, the boundary position of the system satisfies its constraints. Furthermore, the simulation results verify the effectiveness of the proposed control method.

This paper investigates the robust global attitude stabilization problem for a rigid-body system using quaternion-based feedback. We propose a novel synergistic hybrid feedback with the following notable features: (1) It demonstrates central synergism by utilizing a minimal number of potential functions; (2) It ensures consistency with respect to the unit quaternion representation of rigid-body attitude; (3) Its state-feedback laws incorporate a shared action term that steers the system towards the desired attitude. We demonstrate that the proposed hybrid feedback method effectively solves the problem at hand and guarantees robust uniform global asymptotic stability.

The evolution of interpersonal relationships to structural balance involves various complex social psychological mechanics, including interpersonal influences, opinion dynamics, person–person homophily, person–entity homophily, etc. In this paper, we propose a discrete-time nonlinear dynamical system that characterizes the complex interplay among all the above mechanisms. Specifically, interpersonal appraisals are updated based on person–person homophily and person–opinion homophily; the social influence matrix is built according to the interpersonal appraisals; and the opinion dynamics evolve on the social influence network. Via theoretical analysis, we characterize the finite-time behavior and the equilibrium set of the model. In addition, we establish the equivalence among social balance, modulus consensus, convergence, and the non-vanishing appraisal condition. Moreover, we provide sufficient conditions such that the current faction formation in social balance is changed by introducing additional opinion dimensions, i.e., by setting new agendas. Numerical examples show the effectiveness of such agenda-setting strategy and indicate that sufficiently extreme topics are required in order to successfully conduct such manipulation.

Structural symmetries of linear dynamical systems can be exploited for decoupling the dynamics and reducing the computational complexity of the controller implementation. However, in practical applications, inexact structural symmetries undermine the ability to decouple the system, resulting in the loss of any potential complexity reduction. To address this, we propose substituting an approximation with exact structural symmetries for the original system model, thereby introducing an approximation error. We focus on internal model controllers for cross-directional systems encountered in large-scale and high-speed control problems of synchrotrons or the process industry and characterise the stability, performance, and robustness properties of the resulting closed loop. While existing approaches replace the original system model with one that minimises the Frobenius norm of the approximation error, we show that this can lead to instability or poor performance. Instead, we propose approximations that are obtained from semidefinite programming problems. We show that our proposed approximations can yield stable systems even when the Frobenius norm approximation does not. The paper concludes with numerical examples and a case study of a synchrotron light source with inexact structural symmetries. Exploiting structural symmetries in large-scale and high-speed systems enables faster sampling times and the use of more advanced control techniques, even when the symmetries are approximate.

This paper studies the problem of safe stabilization of control-affine systems under uncertainty. Our starting point is the availability of worst-case or probabilistic error descriptions for the dynamics, a control barrier function (CBF) and a control Lyapunov function (CLF). These descriptions give rise to second-order cone constraints (SOCCs) whose simultaneous satisfaction guarantees safe stabilization. We study the feasibility of such SOCCs and the regularity properties of various controllers satisfying them.