Optimal stationary control of diesel engines using periodic control

Measurements and optimal control are used to study whether the fuel economy of a diesel engine can be improved through periodic control of the wastegate, illustrating how modern optimal control tools can be used to identify non-trivial solutions that can improve performance. The measurements show that the pumping torque of the engine is changed when the wastegate is controlled in a periodic manner versus stationary even if the mean position is the same. If this decreases the fuel consumption or not is seen to be frequency and operating point dependent. The measurements indicate that the phenomenon occurs in the time scales capturable by mean value engine models (MVEM). The operating points are further analyzed using a MVEM and optimal control. It is shown that whether the optimal solution exhibits periodic oscillations or not is operating point dependent, but is not due to the instantaneous nature of the controls. Even if an actuator model is added the oscillations persist for reasonable time constants, the frequency of the oscillations is however affected. Further it is shown that the periodic control can be predicted by optimal periodic control theory and that the frequency of the control affects the resulting efficiency.

On controlled one-dimensional diffusion processes with unknown parameter

We consider a controlled diffusion process, the description of which depends on an unknown parameter α, and investigate the following control policy. To each α an optimal stationary control is associated. α is estimated recurrently from the trajectory by Bayes' method, and the optimal stationary control corresponding to the estimate is used. We establish the consistency of the estimate, and present asymptotic properties of the criterion function. They follow from the central limit theorem, from the law of large numbers and from the law of the iterated logarithm for local martingales.

On controlled one-dimensional diffusion processes with unknown parameter

We consider a controlled diffusion process, the description of which depends on an unknown parameter α, and investigate the following control policy. To each α an optimal stationary control is associated. α is estimated recurrently from the trajectory by Bayes' method, and the optimal stationary control corresponding to the estimate is used. We establish the consistency of the estimate, and present asymptotic properties of the criterion function. They follow from the central limit theorem, from the law of large numbers and from the law of the iterated logarithm for local martingales.

Estimation and control in Markov chains

We consider a finite controlled Markov chain, the description of which depends on an unknown parameter a, and investigate the following control policy. To each a an optimal stationary control is associated. a is estimated recurrently from the trajectory by the minimum contrast method, and the optimal stationary control corresponding to the estimate is used. We present asymptotic properties of the estimate and of the criterion function. They follow from the law of large numbers and from the central limit theorem for controlled Markov chains derived with the aid of martingales.

Estimation and control in Markov chains

We consider a finite controlled Markov chain, the description of which depends on an unknown parameter a, and investigate the following control policy. To each a an optimal stationary control is associated. a is estimated recurrently from the trajectory by the minimum contrast method, and the optimal stationary control corresponding to the estimate is used. We present asymptotic properties of the estimate and of the criterion function. They follow from the law of large numbers and from the central limit theorem for controlled Markov chains derived with the aid of martingales.