Robin Hill

Nonlinear control law for aerial towed target

The control law for a maneuverable towed target is derived using inversion of nonlinear dynamic and kinematic equations of motion that take the cable tension force into account. Dynamic properties of the states allowed for construction of lower order subsystems with different time scales for their variables. These faster and slower parts were inverted consecutively to control flight-path angles of the towed vehicle. A procedure is described for estimation of the aerodynamic and tension forces acting on the target and states unavailable for direct measurements from a conventional set of feedback parameters. Guidance and station-keeping properties of the control law are demonstrated by simulation results.

Pole assignment with robust stability

This paper uses convex analysis for the pole assignment design of discrete-time SISO systems incorporating robust stability against norm bounded parametric perturbations in the plant transfer function. The method involves designing an overparameterized pole assignment controller for the nominal plant with the overparameterization chosen to reduce the size of changes in the closed-loop characteristic equation which result from plant perturbations. Sufficiency bounds on the l/sub p/ norm of the perturbation guaranteeing stability are obtained. >

Dual periodicity in l1-norm minimisation problems

The topic of this paper is the discrete-time l1-norm minimisation problem with convolution constraints. We find primal initial conditions for which the dual optimal solution is periodic. Periodicity of the dual optimal solution implies satisfaction of a simple linear recurrence relation by the primal optimal solution.

Linear Programming and l 1 -Norm Minimization Problems with Convolution Constraints

We illustrate some recent results on exact solutions to discrete-time l1-norm minimization problems with convolution constraints. A fixed-point property for this class of problems is introduced. The convolution constraints can be interpreted as a dynamic system with initial conditions. We show by construction that optimal solutions with a rational Z-transform exist for any initial conditions satisfying the fixed-point property. Some fixed-point initial conditions satisfy a further stability property. If there exists a stable fixed point, then for any initial condition in some neighbourhood of the fixed point an optimal solution can be constructed having a rational Z-transform.

Companion matrices and their relations to Toeplitz and Hankel matrices

Abstract In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices, preserving the Toeplitz or Hankel structure respectively.

Exact solutions to a two-block l1 optimal control problem

Abstract In this paper we illustrate some new ideas in the theory of l 1 –norm minimisation. A simple looking mathematical programming problem, namely the minimisation of the sum of the one norms of two signals connected by convolution constraints, is investigated. This describes an l 1 model matching problem for which there are no zero interpolation conditions, and just one rank interpolation condition. Despite its apparent simplicity, finding exact solutions for this problem is a challenging task. We extend the class of problems for which exact optimal solutions can be found by combining a primal/dual formulation with dynamic programming ideas. These solutions have the desirable feature of yielding a control law in feedback form.

Comments on "Controller design with multiple objectives"

We point out that the proof of one of the theorems presented in the above paper by Elia et al. (see ibid. vol.42 (1997)) is invalid and provide a correct proof. The flawed proof is long and complex, and incorrectly tries to make use of duality results via a version of the Lagrange multiplier theorem. The proof we presented, based on an elementary convexity argument, is very simple.

Fault detection and identification-A filter investigation: Fault detection and identification-a filter investigation

This paper develops a new active fault-tolerant control system based on the concept of analytical redundancy. The novel design presented here consists of an observation filter-based fault detection and identification system integrated with a nonlinear model predictive controller. A number of observation filters are designed, integrated with the nonlinear controller, and tested before reaching the final design, which comprises an unscented Kalman filter for fault detection and identification together with a nonlinear model predictive controller to form an active fault-tolerant control system.

Exact recursive updating of state uncertainty sets for linear SISO systems

Abstract This paper addresses the classical problem of determining the set of possible states of a linear discrete-time SISO system subject to bounded disturbances, from measurements corrupted by bounded noise. These so-called uncertainty sets evolve with time as new measurements become available. We present two theorems which give a complete description of the relationship between uncertainty sets at two successive time instants, and this yields an efficient algorithm for recursively updating uncertainty sets. Numerical simulations demonstrate performance improvements over existing exact methods.

Convergence of truncates in l1 optimal feedback control 61

Existing design methodologies based on infinite-dimensional linear programming generally require an iterative process often involving progressive increase of truncation length, in order to achieve a desired accuracy. In this chapter we consider the fundamental problem of determining a priori estimates of the truncation length sufficient for attainment of a given accuracy in the optimal objective value of certain infinite-dimensional linear programs arising in optimal feedback control. The treatment here also allows us to consider objective functions lacking interiority of domain, a problem which often arises in practice.