Adaptive Control Brief History Adapt at ion and feed back Early flig ht co nt rol systems 1955 Truxal 1959: Desig ned from an adaptive Dy namic program ming Bellman 1957 Dual cont rol Feld baum 1960 . EEE CSS Committee 1973 System ident ificat io n 1965- Self-organizing co nt rol process SOC Learning co nt rol Tsypkin 1971 Parameter adaptive soc Perfor ma nce adaptive soc Algorit hms MRAS STR 1970 Learning co nt rol system Stability analysis 1980 Prag mat ically: A special class of nonlinear Robust ness 1985 cont rol systems Ind ust rial products 1982 Linear Feed back-2DOF Feedforward Feedback Process An Adaptive Control system G adjustment Controller Setpoint Two-degree-of-freedo m struct ure(FB+FF) Controller Plant The sensit iv ity funct io n and co mplement ary sensitivity function 1+G, Gb 1+L Yol(s) PgB 1+ GpGrb 1+L Reg ular feed back loop L= GPGfb is the loop transfer function. Para meter adjust ment loop s+T=l and dT 1 dG C K. J. Ast ro m and B. WittenmarkAdaptive Control  Adaptation and feedback  Truxal 1959:Designed from an adaptive view point  IEEE CSS Committee 1973: { Self-organizing control process SOC { Parameter adaptive SOC { Performance adaptive SOC { Learning control system  Pragmatically: A special class of nonlinear control systems Brief History  Early ight control systems 1955 {  Dynamic programming Bellman 1957  Dual control Feldbaum 1960  System identication 1965 {  Learning control Tsypkin 1971  Algorithms MRAS STR 1970 {  Stability analysis 1980 {  Robustness 1985 {  Industrial products 1982 { An Adaptive Control System Parameter adjustment Controller Plant Controller parameters Control signal Output Setpoint Notice two loops  Regular feedback loop  Parameter adjustment loop Linear Feedback - 2DOF Feedforward Process u y Feedback −1 uc ym Gfb Gff Σ Gp Two-degree-of-freedom structure (FB+FF) The sensitivity function and complementary sensitivity function S = 1 1 + GpGf b = 1 1 + L = Ycl (s) Yol (s) T = GpGf b 1 + GpGf b = L 1 + L L = GpGf b is the loop transfer function, S + T = 1 and dT T = 1 1 + GpGf b dGp Gp = S c K. J. Åström and B. Wittenmark 2