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In this paper, we analyse some fundamental structural properties of linear time-invariant multivariable systems in the controller canonical form and present a direct method for the computation of bases and associated friends for output-nulling, input-containing and reachability subspaces in terms of the parameters of the system and the invariant zero structure, both in the nondefective and in the defective case. Using this analysis, it is possible to express the solvability conditions of important control and estimation problems in terms of easily checkable conditions on the system matrices.

For linear, time-invariant, stabilizable multivariable systems, we examine the problem of the existence and computation of proper denominator assigning and internally stabilizing feedback compensators, which give rise to a closed-loop system, whose transfer function matrix is equal to one that can be obtained by the action of state variable feedback. We establish a sufficient condition for the solution of this problem for the class of systems with the same number of inputs and outputs and non-singular transfer function matrix with all its zeros located in the open left half of the complex plane.

In this paper, we employ the Rosenbrock system matrix pencil to find and parameterise regular friends of output-nulling and reachability subspaces of linear, time-invariant descriptor systems, which yield nonzero characteristic polynomial and assign the corresponding closed-loop finite eigenstructure. In particular, we consider impulse controllable descriptor systems and the computation of these friends is done in such a way to also eliminate impulsive behaviour.

This paper presents a novel control design procedure for simultaneous course keeping and rudder roll stabilisation for a surface marine craft. We address the design using the Internal Model Principle. This approach has been used to analyse fundamental limitations of rudder roll stabilisation due to unstable zero dynamics, but it has not been exploited for full control system design. The design is based on roll sensitivity shaping and uses a simplified parametric model of the roll-induced wave motion. This design provides opportunities for adapting the performance due to changes in environmental and sailing conditions. This is a need driven by a well-known issue leading to performance degradation in this control problem, which is due to the presence of unstable zero dynamics and significant changes in the power spectrum of the disturbance.

In this paper, we investigate an inverse differential game approach to modelling the mid-air collision avoidance behaviours of birds. We propose a general method for estimating the cost-functional parameters of a noncooperative differential game from partial-state measurements of an open-loop Nash equilibrium. We apply the method to data of birds performing mid-air collision avoidance. Our analysis suggests that a differential game model provides a close description of the observed bird behaviours, and could provide new insights for the design of collision avoidance strategies for unmanned aircraft.

The use of linear multivariable feedback control to achieve a nonovershooting step response is considered for multi-input multi-output (MIMO) linear time-invariant (LTI) descriptor systems. The use of dynamic output feedback control to improve the transient response to a step input is also considered for MIMO and LTI descriptor systems. We design a state feedback controller and a dynamic output feedback for MIMO and LTI descriptor systems to asymptotically stabilise and track a step reference with zero overshoot and arbitrarily small rise time, under some mild assumptions.

In this paper, we propose tuning methods for a classical nonlinear dynamic positioning (DP) controller, based on a nested velocity and position feedback structure, for a marine craft moving in the horizontal plane. In particular, the problem is considered for fully-actuated marine craft. We describe the main characteristics of the DP problem and review the basic architecture of a classical DP system with nested loops. Then we design two DP control schemes: diagonally decoupling, and diagonal controller, and propose tuning methods for the controllers, based on pole assignment and numerical optimisation. The performance and robustness of the designed controllers are compared through simulations for an autonomous underwater vehicle.

In this paper, we adopt eigenstructure assignment in order to assist with the tuning of a nonlinear energy-based regulator for the positioning of a marine craft in the horizontal plane. The control law is designed using interconnection and damping assignment passivity-based control (IDA-PBC), which results in passive target dynamics that can be expressed as a port-Hamiltonian system (PHS). IDA-PBC has been applied before with success in a number of different applications. To date, however, there has been minimal development in either tuning tools or techniques that can analytically aid the designer in achieving the desired response characteristics. Good results can be achieved only with intuitive and meticulous manual tuning. By linearising the nonlinear target dynamics in PHS form, we demonstrate that the analysis of the eigenstructure, and consequently its assignment can significantly aid the tuning process. The approach provides a mechanism for simultaneously considering the frequency domain characteristics at a point of linearisation, as well as the time domain characteristics. A demonstration of the method is provided in the form of a design study for position regulation of an underwater vehicle in the horizontal plane.

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary

A result originally reported by Hammer for linear time invariant (LTI) single input-single output systems and concerning an invariant and a canonical form of the transfer function matrix of the closed loop system under dynamic feedback compensation is generalized for LTI multivariable systems. Based on this result, we characterize the class of transfer function matrices that are obtainable from an open loop transfer function matrix via the use of proper dynamic feedback compensators and show that if the closed loop transfer function matrix Pc(s) has a desired denominator polynomial matrix which satisfies a certain sufficient condition, then there exists a proper compensator giving rise to an internally stable closed loop system, whose transfer function matrix is Pc(s).

This paper investigates the robust H infin control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

In this paper, we investigate several theoretical and computational aspects of fundamental subspaces for linear, time-invariant (LTI) descriptor systems, which appear in the solution of many control and estimation problems. Different types of reachability and controllability for descriptor systems are described and discussed. The Rosenbrock system matrix pencil is employed for the computation of supremal output-nulling subspaces and supremal output-nulling reachability subspaces for descriptor systems.

This paper deals with the computation of basis matrices of output-nulling and reachability subspaces for linear time-invariant (LTI) descriptor systems, which have been found to appear in the solution of many control and estimation problems. In particular, one of the classic approaches for the computation of these subspaces, which exploits the calculation of the null-space of the Rosenbrock system matrix pencil and which has found important applications in non-interacting and fault-detection problems, is generalized for descriptor systems.

This paper describes a concept for a collision avoidance system for ships, which is based on model predictive control. A finite set of alternative control behaviors are generated by varying two parameters: offsets to the guidance course angle commanded to the autopilot and changes to the propulsion command ranging from nominal speed to full reverse. Using simulated predictions of the trajectories of the obstacles and ship, compliance with the Convention on the International Regulations for Preventing Collisions at Sea and collision hazards associated with each of the alternative control behaviors are evaluated on a finite prediction horizon, and the optimal control behavior is selected. Robustness to sensing error, predicted obstacle behavior, and environmental conditions can be ensured by evaluating multiple scenarios for each control behavior. The method is conceptually and computationally simple and yet quite versatile as it can account for the dynamics of the ship, the dynamics of the steering and propulsion system, forces due to wind and ocean current, and any number of obstacles. Simulations show that the method is effective and can manage complex scenarios with multiple dynamic obstacles and uncertainty associated with sensors and predictions. This is the authors' accepted and refereed manuscript to the article. © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper we analyse the geometric properties of systems in the controller canonical form. We show that using a technique based on the calculation of null-spaces of the Rosenbrock system matrix pencil facilitates the computation of the fundamental geometric subspaces for such systems. It is also shown how this geometric analysis can be exploited to derive necessary and sufficient conditions for the solution of the global monotonic tracking control problem solely in terms of the problem data.

Exploiting wind-energy is one possible way to extend the flight duration of an Unmanned Aerial Vehicle. Wind-energy can also be used to minimise energy consumption for a planned path. In this paper, we consider uncertain, time-varying wind fields and plan a path through them that exploits the energy the field provides. A Gaussian distribution is used to determine uncertainty in the time-varying wind fields. We use a Markov Decision Process to plan a path based upon the uncertainty of the Gaussian distribution. Simulation results are presented to compare the direct line of flight between a start and target point with our planned path for energy consumption and time of travel. The result of our method is a robust path using the most visited cell while sampling the Gaussian distribution of the wind field in each cell.