Les S. Jennings

On the use of spline functions for data smoothing

Abstract The appropriateness of various numerical procedures for obtaining valid time-derivative data recently reported in the literature (Zernicke et al. , 1976; McLaughlin et al. , 1977; Pezzack et al. , 1977) is discussed. A case for the use of quintic natural splines is presented, based on the smoothness of higher derivatives and flexibility in application.

A new computational algorithm for functional inequality constrained optimization problems

Abstract In this note, a computational algorithm is devised for solving a class of functional inequality constrained optimization problems, based on a penalty function. For illustration, a numerical example is solved.

Brief Control parametrization enhancing technique for optimal discrete-valued control problems

In this paper, we consider a class of optimal discrete-valued control problems. Since the range set of the control function is a discrete set and hence not convex. These problems are, in fact, nonlinear combinatorial optimization problems. Using the novel idea of the control parametrization enhancing technique, it is shown that optimal discrete-valued control problems are equivalent to optimal control problems involving a new control function which is piecewise constant with pre-fixed switching points. The transformed problems are essentially optimal parameter selection problems and can hence be readily solved by various existing algorithms. A practical numerical example is solved using the proposed method.

Functional Observability and the Design of Minimum Order Linear Functional Observers

The design of a minimum-order linear functional observer for linear time-invariant systems has been an open problem for over four decades. This technical note provides a solution to this problem. The technical note also introduces the concept of Functional Observability/Detectability and shows that the well-known concept of Observability/Detectability is a special case of Functional Observability/Detectability.

Computational Discretization Algorithms for Functional Inequality Constrained Optimization

In this paper, a functional inequality constrained optimization problem is studied using a discretization method and an adaptive scheme. The problem is discretized by partitioning the interval of the independent parameter. Two methods are investigated as to how to treat the discretized optimization problem. The discretization problem is firstly converted into an optimization problem with a single nonsmooth equality constraint. Since the obtained equality constraint is nonsmooth and does not satisfy the usual constraint qualification condition, relaxation and smoothing techniques are used to approximate the equality constraint via a smooth inequality constraint. This leads to a sequence of approximate smooth optimization problems with one constraint. An adaptive scheme is incorporated into the method to facilitate the computation of the sum in the inequality constraint. The second method is to apply an adaptive scheme directly to the discretization problem. Thus a sequence of optimization problems with a small number of inequality constraints are obtained. Convergence analysis for both methods is established. Numerical examples show that each of the two proposed methods has its own advantages and disadvantages over the other.

Numerical Solution of Hamilton-Jacobi-Bellman Equations by an Upwind Finite Volume Method

In this paper we present a finite volume method for solving Hamilton-Jacobi-Bellman(HJB) equations governing a class of optimal feedback control problems. This method is based on a finite volume discretization in state space coupled with an upwind finite difference technique, and on an implicit backward Euler finite differencing in time, which is absolutely stable. It is shown that the system matrix of the resulting discrete equation is an M-matrix. To show the effectiveness of this approach, numerical experiments on test problems with up to three states and two control variables were performed. The numerical results show that the method yields accurate approximate solutions to both the control and the state variables.

Performance objectives in human movement: A review and application to the stance phase of normal walking ☆

Abstract That some form of optimisation takes place in skilled human movements may be inferred from metabolic, electromyographic and perceptual experimental results. However, the parameter(s) or function(s) minimised in activities such as walking has not been satisfactorily identified. This work used non-linear optimal control and multiple-segment simulation software to evaluate the predictive ability of seven performance objective functions. The results indicated that minimisation of the time integrals of the sums of the joint torques, the segmental angular accelerations, or the segmental mechanical energies produced the best simulations of the single stance phase of walking. Strong support was also provided for the existence of simultaneous multiple performance objectives in complex movements.

Existence Conditions for Functional Observability From an Eigenspace Perspective

Two theorems on conditions for nonexistence and for existence, of built functional observers, from an eigenspace perspective are presented and proved. One more theorem on Functional Observability in terms of constructed products of matrices A,C and L0 is also presented. This theorem provides an easy way to check Functional Observability before proceeding with the design of functional observers. The existence and the nonexistence theorems are used to unify previously reported theorems on Functional Observability by showing their equivalence. The connection between the concept of Functional Observability and the well known concept of State Observability is also presented.

A multivariate adaptive regression B-spline algorithm (BMARS) for solving a class of nonlinear optimal feedback control problems

In this paper we present a novel method for solving a class of nonlinear optimal feedback control problems with moderately high dimensional state spaces, based on an adapted version of the BMARS algorithm. Numerical experiments were performed using problems with up to six state variables. The numerical results clearly demonstrate the efficiency and potential of the method for solving high dimensional problems.

Generality of functional observer structures

Functional observers estimate a linear function of the state vector directly without having to estimate all the individual states. In the past various observer structures have been employed to design such functional estimates. In this paper we discuss the generality of those various observer structures and prove the conditions under which those observer structures are unified. The paper also highlights and clarifies the need to remove the self-convergent states from the system and also from the functions to be estimated before proceeding with the design of a functional observer or else incorrect conclusions regarding the existence of functional observers can be arrived at.