Introduction re Stochastic self- Tuners self-tuning regulator 1.Introduct ion EStimation 2. Minimum variance co nt ro Controller 3. Est imat ion of noise models parameters 4. Stochast ic self-tuners Controller Process 5. Feedforward cont rol 6. P redict ive co nt rol 7. Conclusio ns nt eresting res ults Here An e amp Process dynamics y(t+1)+ay(t)=bu(t)+e(t+1)+ce(t) If parameters are know n the co nt rol law is Mini mum Variance and Moving Average Control u(t)=-y(t) b,3(t . Motivat io n The output then beco mes yt=et . The general case Notice Out put is white noise Innovations represent ation of c< 1 C K.J. Ast ro m and B WittenmarkStochastic Self-Tuners 1. Introduction 2. Minimum variance control 3. Estimation of noise models 4. Stochastic Self-tuners 5. Feedforward control 6. Predictive control 7. Conclusions Introduction Same idea as before Process parameters Controller design Estimation Controller Process Controller parameters Reference Input Output Specification Self-tuning regulator But now use  Design based on stochastic control theory  Some very interesting results  Here is where it started Minimum Variance and Moving Average Control  Motivation  An Example  The General Case An Example Process dynamics y(t + 1) + ay(t) = bu(t) + e(t + 1) + ce(t) If parameters are known the control law is u(t) = ￾y(t) = ￾ c ￾ a b ; y(t) The output then becomes y(t) = e(t) Notice  Output is white noise  Prediction very simple with the model  Innovations representation  Importance of jcj < 1 c K. J. Åström and B. Wittenmark 1