The problem of providing optimal regulation of non-linear systems has been one of long standing and has been solved usually by empirical techniques with, seemingly, no relief provided by the methods based on the newer theories of control. This paper deals with two methods which both depend on the solution of an optimal control problem, and which take into account the specifically non-linear nature of the plant. The sub-optimal control laws which result are linear and are easily synthesised.
BellmanR.KalabaR. E.1965. Quasilinearisation and Nonlinear Boundary Value Problems. Elsevier, NY.
3.
BeltramiE. J.1970. An Algorithmic Approach to Nonlinear Analysis and Optimisation. Academic Press, NY.
4.
BurghartJ. G.1969. ‘A technique for sub-optimal feedback control of non-linear systems’. Trans IEEE, Vol AC-14, No 10, 530–533.
5.
d'AzzoJ. J.HoupisC. H.1975. Linear Control System Analysis and Design: Conventional and Modern. McGraw-Hill.
6.
DebsA. S.AthansM.1970. ‘On average-optimal nonlinear feedback control systems’. JACC, Paper 21-A, 524–534.
7.
EisenbergB. R.SageA. P.1966. ‘Closed loop optimisation of fixed configuration systems’. Int J Cont, Vol 3, No 2, 183–194.
8.
FalbP. L.de JongJ. L.1969. Some Successive Approximation Methods in Control and Oscillation Theory. Academic Press, NY.
9.
FooteA. L.1972. ‘Truncated power series control representations for optimisation of dynamic systems’. AFAL, TR-191, Aug.
10.
GarrardW. L.1969. ‘Additional results on sub-optimal feedback control of linear systems’. Int J Cont, Vol 10, No 6, 657–663.
11.
GustafsonR. D.HarwoodR. A.1969. ‘Nonlinear optimal control by use of extra linear states to represent non-linearities’. Trans ASME, J Bas Eng, Vol 91, Ser D, No 2, 139–148.
KleinmanD. L.1968. ‘On an iterative technique for Riccati equation computations’. Trans IEEE, Vol AC-13, No 1, 114–115.
14.
LeeE. S.1968. Quasilinearisation and Invariant Imbedding. Academic Press, NY.
15.
LukesD. L.1969. ‘Optimal regulation of nonlinear dynamical systems’. SIAMJ Cont, Vol 7, No 1, 75–100.
16.
MarshallS. A.NicholsonH.1970. ‘Optimal control of linear multivariable systems with quadratic performance criteria’. Proc IEE, Vol 117, No 8, 1705–1713.
17.
MichaelG. J.BelluardoR.1971. ‘Analytic synthesis of optimal nonlinear feedback control’. JACC, Paper 7-C5, 665–670.
18.
MieleA. A.NaqviS.LevyA. V.IyerR. R.1971. ‘Numerical solution of non-linear equations and nonlinear two point boundary value problems’. Advances in Control, 8, 189–215, Academic Press, NY.
19.
NicholsonH.1964. ‘Dynamic optimisation of a boiler’. Proc IEE, Vol III, No 8, 1479–1499.
20.
RadbillJ. R.McCueG. A.1971. Quasilinearisation and Nonlinear Problems in Fluid and Orbital Mechanics. Elsevier, NY.
21.
RobertsS. M.ShipmanJ. S.1972. Two Point Boundary Value Problems — Shooting Methods. Elsevier, NY.
22.
SalmondM.KokotovicP. V.1969. ‘Design of linear controllers for non-linear plants’. Trans IEEE, Vol AC-14, No 6, 289–292.
23.
WhiteR. R.CookG.1973. ‘Use of piecewise linearisation for sub-optimal control of non-linear systems’. Int J Cont, Vol 18, No 2, 385–397.
