A reduction technique for Generalised Riccati Difference Equations

This paper proposes a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalised discrete algebraic Riccati equation. In particular, an analysis on the eigen- structure of the corresponding extended symplectic pencil enables to identify a subspace in which all the solutions of the generalised discrete algebraic Riccati equation are coin- cident. This subspace is the key to derive a decomposition technique for the generalised Riccati difference equation that isolates its nilpotent part, which becomes constant in a number of steps equal to the nilpotency index of the closed-loop, from another part that can be computed by iterating a reduced-order generalised Riccati difference equation

The extended symplectic pencil and the finite-horizon LQ problem with two-sided boundary conditions

This note introduces a new analytic approach to the solution of a very general class of finite-horizon optimal control problems formulated for discrete-time systems. This approach provides a parametric expression for the optimal control sequences, as well as the corresponding optimal state trajectories, by exploiting a new decomposition of the so-called extended symplectic pencil. Importantly, the results established in this paper hold under assumptions that are weaker than the ones considered in the literature so far. Indeed, this approach does not require neither the regularity of the symplectic pencil, nor the modulus controllability of the underlying system. In the development of the approach presented in this paper, several ancillary results of independent interest on generalised Riccati equations and on the eigenstructure of the extended symplectic pencil will also be presented

The role of the generalised continuous algebraic Riccati equation in impulse-free continuous-time singular LQ optimal control

In this paper the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control is analysed. To date, the importance of the continuous-time generalised Riccati equation in the context of optimal control has not been understood. This note addresses this point. We show in particular that when the continuous-time (constrained) generalised Riccati equation admits a symmetric solution, the corresponding linear-quadratic (LQ) problem admits an impulse-free optimal control

The generalised discrete algebraic Riccati equation arising in LQ optimal control problems: Part II

In this paper we develop an analytic approach to the solution of a very general class of discrete finite horizon optimal control problems. This method hinges on a new decomposition of the so-called extended symplectic pencil. Interestingly, the results established in this paper hold under assumptions that are weaker than the ones considered in the literature so far

Unified control parametrisation approach for finite-horizon feedback control with trajectory shaping

This study presents control parametrisation as a unifying framework for designing a linear feedback control law that achieves finite-time transfer of output as well as trajectory shaping. Representing control input as a linear combination of independent basis functions allows wide variability in the resultant feedback control laws through selection of the number and types of basis functions. Given an array of basis functions that meets the trajectory shaping necessities, the unified design approach proceeds with determination of the coefficients so that the predicted trajectory attains the desired output at the final time. The input evaluated with the coefficients found at each instance essentially turns out to be a linear state feedback policy with an additional feedforward term and time-dependent gains which is appropriate for practical use. The unified control parametrisation approach lends itself well to missile guidance applications with the expandability and direct trajectory shaping capability that it provides. To emphasise expandability of the framework, this study revisits the trajectory shaping guidance laws from the control parametrisation viewpoint and shows how the notion of specifying input basis functions not only generalises various existing methods but also enables further extensions. Furthermore, an application to integrated guidance and control illustrates the strength of design process in handling the shaping requirements more directly through construction of appropriate basis

A unified approach to the finite-horizon linear quadratic optimal control problem

Under the mild assumption of sign-controllability, a closed-form expression parameterizing all the solutions of the Hamiltonian differential equation over a finite time interval is presented in terms of a strongly unmixed solution of an algebraic Riccati equation (ARE) and of the solution of an algebraic Lyapunov equation. This result is employed for the solution of a generalized version of the finite-horizon linear quadratic (LQ) problem, encompassing the case of fixed end-point. Furthermore, it is shown how this method can be applied to the H_2 preview decoupling problem

A vision-based optical character recognition system for real-time identification of tractors in a port container terminal

Automation has been seen as a promising solution to increase the productivity of modern sea port container terminals. The potential of increase in throughput, work efficiency and reduction of labor cost have lured stick holders to strive for the introduction of automation in the overall terminal operation. A specific container handling process that is readily amenable to automation is the deployment and control of gantry cranes in the container yard of a container terminal where typical operations of truck identification, loading and unloading containers, and job management are primarily performed manually in a typical terminal. To facilitate the overall automation of the gantry crane operation, we devised an approach for the real-time identification of tractors through the recognition of the corresponding number plates that are located on top of the tractor cabin. With this crucial piece of information, remote or automated yard operations can then be performed. A machine vision-based system is introduced whereby these number plates are read and identified in real-time while the tractors are operating in the terminal. In this paper, we present the design and implementation of the system and highlight the major difficulties encountered including the recognition of character information printed on the number plates due to poor image integrity. Working solutions are proposed to address these problems which are incorporated in the overall identification system.postprin