A method of solving finite-horizon optimal control problems involving a class of discrete-time rational systems is proposed. A sequence of algebraic equations for the unknown costate at each time is constructed backward, starting from the terminal condition, by using the recursive substitution of mappings in the optimality conditions. This recursive substitution can be viewed as a generalization of a classical solution to finite-horizon linear quadratic control by means of a transition matrix. The existence and uniqueness of locally optimal state feedback laws defined via algebraic equations for the costates can be guaranteed if second-order sufficient conditions for optimality hold along a nominal trajectory.
This paper proposes motion-trajectory generation for mechanical systems that can be widely used in industrial applications. Many industrial systems, such as feed drive tables, gantry cranes, and material handling systems, are operated using S-curve acceleration and deceleration trajectory, and simple controllers that allow only such a simple motion trajectory are employed from the viewpoints of controller hardware and implementation cost efficiency. This study deals with simple mechanical dynamics including vibration properties and derives a necessary and sufficient condition for the motion trajectory to suppress residual vibration. Simulation and experimental results demonstrate the validity of the proposed conditions.
This paper proposes an engine speed tracking controller based on the MPC scheme and investigates a tuning method for the practical control performance from the viewpoint of the ILQ design. First, the nonlinear system dynamics based on the engine mean-value model is transformed to the linear tracking error dynamics by the feedback linearization method. Then the MPC speed tracking controller is designed based on the derived tracking error dynamical model. To achieve the convenient adjustment of the control performance, the quadratic weightings in MPC performance index are calculated with respect to a single tuning parameter by means of the inverse optimality conditions of the LQ optimal problem. Moreover, an adaptive compensator is introduced to guarantee the control precision even if the predictive model is not very accurate. Experiments are conducted in the 3.5L-V6 gasoline engine test bed, the results demonstrate the good control effects for speed tracking by the proposed MPC controller and also confirm the validity of the proposed tuning approach.
A problem in the field of nonlinear dynamics is considered with a technique of control theory. In particular, for preventing a nonlinear dynamical system from making undesirable bifurcation, it is proposed to control its parameter with a stability index and a matrix inequality. A basic idea is to update the parameter of the system so as to minimize the stability index. Since the stability index is not differentiable as a function of the parameter, its minimization is carried out through equivalent transformation to a smooth minimization problem, where a matrix inequality is used. The proposed method is applied to a simple dynamical system and shown to be effective. Its generalization is also considered for driving a system to avoid chaos.
A continuous annealing line is the process which consists of heating, soaking and cooling of steel strips. In this process, it is very significant to control steel strip temperature and tension. If the steel strip temperature or tension is not controlled properly, it may cause unstable operations and, in the worst case, result in the trouble such as buckling of the steel strip. Once buckling occurs, it takes very long time to recover the process line and the productivity decreases. Therefore it is necessary to prevent these troubles by detecting signs of buckling as early as possible. While many trials to clarify the mechanism of buckling based on physical approaches were conducted in the past, it cannot find any appropriate technique with sufficient accuracy. For the above reason, data oriented approaches such as statistic analysis are studied as an alternative to the conventional monitoring method. In this paper, a new monitoring method for detecting buckling in continuous annealing lines is proposed based on canonical correlation analysis. It can extract not only relations among variables such as the strip temperature and tension but also the ones in the longitudinal direction of the strip and monitor changes of these relations. The off-line numerical tests are conducted and effectiveness of the proposed method is confirmed compared to the conventional method.
As the size of systems to be controlled gets larger, distributed optimization is becoming one of the significant topics, where each local optimization problem is solved by an individual computer in parallel and in a synchronize manner to derive a global optimal solution more quickly and robustly than centralized methods. However, most distributed optimization techniques require synchronous communication, where optimization results derived by individual computers are shared at the end of each iteration. This paper proposes a distributed optimization algorithm with event triggered communication where the iterations are synchronized but the communication does not happen in every iteration. Then both synchronous and event triggered algorithms are compared through numerical simulation to show that communication costs drop significantly.
In this paper, we consider global observability decompositions of autonomous polynomial systems by using commutative algebra and algebraic geometry. In contrast to the local observability decomposition, not all globally unobservable systems can be decomposed into globally observable and unobservable subsystems by bijective polynomial mappings. The objective in this paper is giving a sufficient condition for the global observability decomposition of polynomial systems based on conventional global observability conditions and properties of polynomial mappings.
This paper proposes a protocol for a distributed optimization problem to minimize the average of objective functions of the agents in the network with satisfying constraints of each agent. The protocol can handle uncommon constraints of the agents. Instead of invoking dual functions, only 1-bit information on fulfillment of the constraint of each agent is transmitted between agents as well as the decision variable. The proof of consensus and convergence is provided based on the constrained subgradient method. A numerical example illustrates how the proposed protocol works.