This study presents a new robust model predictive control (MPC) scheme for constrained continuous-time non-linear systems subject to unknown but bounded disturbances. The performance index is a function on disturbance-free state and input profiles, and the predictions are parameterised by an analytic controller with a small number of adjustable parameters. In particular, input-to-state stable control Lyapunov functions techniques are used to construct a variation of Freeman's formula with some tunable parameters, which yields an MPC with guaranteed input-to-state stability in some estimated invariant sets w.r.t the disturbance. It is further derived that the MPC here is inverse optimal for a class of dynamic game problems and has a sector margin (0.5, ∞). Finally, two numerical examples are used to illustrate the performance and effectiveness of the results obtained here.

Two-level quantum system (Qubit) and non-classical states of light such as single photon and superposition of coherent state are under special attention in quantum technologies such as quantum computing, quantum communication and quantum computers. Hence, behaviour of two-level system driven by such inputs is important. In this study, the behaviour of two-level quantum system driven by vacuum state, single photon and superposition of coherent state was investigated by assuming Pauli matrices as system operators in quantum filtering equations. The purity of conditioned and unconditioned states is also analysed when the system is driven by different inputs. The results show that the stochastic master equation (ME)dynamic has more information about the status of system than ME dynamic.

This study presents a solution to the problem of cooperative path following of multiple underactuated marine surface vehicles subject to dynamical uncertainties and ocean disturbances. The dedicated control designs are categorised into two envelopes. One is to steer individual underactuated marine surface vehicle to track a given spatial path; and the other is to synchronise the along-path speeds and path variables under the constraints of an underlying communication network in order to hold a desired formation pattern. Within these two formulations, a robust adaptive path-following controller is first designed for individual vehicle based on neural networks and a dynamic surface control (DSC) technique. Then, the along-path speeds and path variables are synchronised to each vehicle owing to the proposed decentralised synchronisation control law building on graph theory and Lyapunov theory. The key features of the developed controllers are that, first, the DSC technique simplifies the controller design by introducing first-order filters and avoids the calculation of derivatives of virtual control signals. Second, the developed controllers with filtering adaptive laws allow for fast learning without generating high-frequency oscillations in control signals. Rigorous theoretical analysis demonstrates that all signals in the closed-loop system are uniformly ultimately bounded. Simulation results are provided to show the efficacy of the proposed method.

This study investigates the consensus control of linear multi-agent systems with communication time delay. Upon exploring certain features of Laplacian matrix, optimal consensus control conditions are identified using semi-discretisation method that develops a mapping of the system response in a finite-dimensional state space. Consensus region and consensus boundary can be obtained by comparing the maximum absolute value of the mapping's eigenvalues with 1. Besides, minimisation of the maximum absolute value of the eigenvalues leads to optimal control gains representing fastest convergence speed. The proposed control only uses relative state information of the system. Numerical simulations validate the proposed control design and show the performance with different control gains and time delays.

An approach for eigenvalue assignment in linear descriptor systems via output feedback is proposed. Sufficient conditions in order that a given set of eigenvalues is assignable are established. Parametric form of the desired output feedback gain matrix is also given. The approach assigns the full number of generalised eigenvalues, guarantees the closed-loop regularity and overcomes the defects of some previous works.

In this study, the authors consider the problem of optimal regional controllability of a distributed bilinear system evolving in a spatial domain Ω. The question is to obtain a bounded feedback control with minimum energy that drives such a system from an initial state to a desired one in finite time, only on a subregion ω of Ω. The purpose of this study is to prove that a regional optimal control exists, and characterised as a solution to an optimality system. Numerical approach is given and successfully illustrated by simulations.

This study presents a new robust filtering method in modelling an active multisensory suspension system with measurement delays and parameteric uncertainties in a state-space dynamical model. To achieve good performance of the system, a new distributed fusion receding horizon filtering frameworks are constructed to couple the continuous dynamics with the multisensory discrete measurements, and to coordinately deal with the parametric uncertainty and time-delays. The novel filtering algorithm is proposed based on the receding horizon strategy, standard mixed continuous-discrete Kalman filtering and discrete Kalman filtering for systems with time-delays in order to achieve high estimation accuracy and stability under parametric uncertainties. The key theoretical contributions of this study are the derivation of the error cross-covariance equations between the local receding horizon filters in order to compute the optimal matrix fusion weights. The high accuracy and efficiency of the new filter are demonstrated through its implementation and performance and then compared to the existing vehicle active suspension system.

Reachability analysis and viability theory play an important role in control synthesis and trajectory analysis of constrained dynamical systems, many methods are known for computing them in low-dimensional non-linear systems, but these well-known methods rely on gridding the state space and hence suffer from the curse of dimensionality. In this study, for systems whose dynamics are described by polynomials, a method based on semi-definite programming is proposed to estimate an invariance kernel with target as large as possible by iteratively searching for Lyapunov-like functions. The proposed methodology is scalable, since the size of the semi-definite programming problem to be solved grows linearly with the system dimension. We test the method on two interesting examples and compare them with some existing methods, the results show that our method is more efficient.

This article mainly studies the problem of the exponential stability for singular systems with two interval time-varying delays. By constructing a modified Lyapunov–Krasovskii functional (LKF) and utilising a convex polyhedron method to estimate the derivative of LKF, some new delay-dependent criteria can be established in terms of linear matrix inequalities. Compared with some existing literatures, the novelties in this study are that the needed decisive variables are fewer and the obtained delay-dependent stability criteria are less conservative. Finally, two illustrative numerical examples are given to show the effectiveness of the derived results.

Formation control for a group of autonomous underwater vehicles (AUVs) is challenging due to the complex systems dynamics and time delay in the cooperative feedback loops. This paper introduces a decoupled design procedure, so that formation controllers designed for particle dynamics can be generalised to formation controllers for fully actuated AUVs with six-degree-of-freedom dynamic models for motions in three-dimensional space. The orientation control and the translation control are first decoupled following a standard inner–outer loop approach. Then, a geometric approach is followed to separate the translation dynamics into formation shape dynamics and formation centre dynamics. Coupling terms between the two portions of the dynamics are treated as perturbations and are tolerated by a robust formation-keeping controller. The controller is also robust to constant bounded time delays. This decoupling procedure simplified the entire design process comparing with other existing approaches with similar goals. Both rigorous theoretical analysis and simulation results are presented to justify the effectiveness of this method.