Andrzej Bartoszewicz

Discrete-time quasi-sliding-mode control strategies

In this paper, discrete-time quasi-sliding-mode control systems are considered. A new definition describing the quasi-sliding mode as a motion of the system, such that its state always remains in a certain band around the sliding hyperplane, is introduced. Then, two novel reaching laws satisfying conditions of the definition are proposed and applied to the design of appropriate linear control strategies which drive the state of the controlled system to a band around the sliding hyperplane. Consequently, the undesirable chattering and high-frequency switching between different values of the control signal are avoided. The strategies, when compared with previously published results, guarantee better robustness, faster error convergence, and improved steady-state accuracy of the system. Furthermore, better performance of the system is achieved using essentially reduced control effort.

A comment on “a time-varying sliding surface for fast and robust tracking control of second-order uncertain systems”

In a recent paper, Seung-Bok Choi, Dong-Won Park and Suhada Jayasuriya (Automatica, 30, 899–904, 1994) have presented a stepwise time-varying sliding surface for variable structure control of a class of second-order uncertain systems. As the surface does not truly guarantee insensitivity of the systems to parameter variations and external disturbances, in this comment we propose a continuously time-varying surface that allows faster tracking and really guarantees robust behaviour of the systems.

LQ Optimal Sliding Mode Supply Policy for Periodic Review Inventory Systems

In this technical note, the problem of inventory management in supply chain is addressed from a control theory perspective. In the analyzed setting, the stock used to satisfy an unknown, time-varying demand can be replenished from several supply sources. The replenishment orders are realized with delay which differs among suppliers and transport alternatives. A novel sliding-mode inventory policy is proposed, which guarantees that the demand is always entirely satisfied from the on-hand stock (yielding zero lost-sales cost), the warehouse capacity is not exceeded (what eliminates the risk of high-cost emergency storage) and ordered goods are not returned to the suppliers. As opposed to the classical, stochastic approaches, the parameters of the proposed controller are selected by minimizing a quadratic cost functional, which ensures an optimal dynamical performance of inventory systems with disparate lead times.

Linear-quadratic optimal control strategy for periodic-review inventory systems

The paper addresses the problem of efficient inventory management in production-inventory systems focusing on the dynamical nature of goods flow process. In the considered systems, the stock used to satisfy an unknown, time-varying demand is replenished either from a single or from multiple supply sources. The replenishment orders issued in each review period are realized with a delay, which differs among the suppliers and transport alternatives. For the analyzed setting, modeled as a discrete-time nth-order deterministic system, a new inventory policy is developed using a strict control-theoretic methodology. In contrast to the classical, stochastic approaches, the proposed control law is obtained by minimizing a quadratic cost functional, which guarantees the optimal dynamical performance of production-inventory systems with (possibly) different lead-time delays in the supply path. The designed policy ensures that the demand is always entirely satisfied from the on-hand stock (yielding zero lost-sales cost) and the warehouse capacity is not exceeded (which eliminates the risk of high-cost emergency storage). The closed-form solution of the linear-quadratic (LQ) optimization problem allows for a straightforward implementation of the developed control strategy in real systems.

Discrete-Time Sliding-Mode Congestion Control in Multisource Communication Networks With Time-Varying Delay

This paper addresses the problem of congestion control in communication networks from a control-theoretic perspective. In this type of complex, dynamical systems, the primary obstacle in the design of efficient control is the delay in the feedback loop which may be subject to significant fluctuations during the control process. This paper presents a new approach to solving the congestion problem in multisource networks, in which each flow is characterized by different and time-varying delay, with the application of discrete-time sliding-mode control. The proposed controller, operating at a network node, guarantees that in the considered networks the packet losses are eliminated and all of the available bandwidth at the node output interface is used for the data transfer. The controller is demonstrated to be robust with respect to the abrupt and unpredictable changes of networking conditions, such as delay and bandwidth variations, which need not be correlated with each other. The controller parameters are selected by minimizing a quadratic cost functional. A closed-form solution of the optimization problem allows for a straightforward and operationally efficient implementation of the proposed congestion control strategy in real network nodes.

ITAE Optimal Sliding Modes for Third-Order Systems With Input Signal and State Constraints

In this note, the design of a time-varying switching plane for the sliding-mode control of the third-order system subject to velocity, acceleration and input signal constraints is considered. Initially, the switching plane passes through the system representative point (RP) in the error state space and then it moves with a constant velocity to the origin of the space. Having reached the origin the plane stops moving and remains fixed. The plane parameters are selected to minimize the integral of the time multiplied by the absolute error (ITAE) without violating velocity, acceleration and input signal constraints. Furthermore, the switching plane is chosen in such a way that the reaching phase is eliminated, insensitivity of the system with reference to the external disturbances and the model uncertainty is guaranteed from the very beginning of the control action and monotonic tracking error convergence to zero is ensured.

Linear-Quadratic Optimal Control of Periodic-Review Perishable Inventory Systems

In this brief, the problem of inventory control in systems with perishable goods is addressed from the control-theoretic perspective. In the analyzed setting, the deteriorating stock used to fulfill unknown, time-varying demand is replenished with delay from a remote supply source. In order to eliminate the threat of the bullwhip effect (amplified demand variations translated to the ordering signal), we propose to use the benefits of linear-quadratic optimal control. In contrast to the earlier approaches to inventory management of perishable goods, mainly based on heuristics and static optimization, we apply formal methodology of discrete-time dynamical optimization, and solve the optimal control problem analytically. This allows us to formulate and strictly prove a number of advantageous properties of the designed controller, e.g., we demonstrate that it ensures full demand satisfaction in the system with arbitrary delay and any bounded demand pattern with unknown statistics. The proposed controller outperforms the classical order-up-to policy in terms of higher service level, smaller holding costs, and smaller order-to-demand variance ratio.

New Switching and Nonswitching Type Reaching Laws for SMC of Discrete Time Systems

In this brief a new switching type reaching law for sliding mode control of discrete time systems is proposed. The proposed reaching law is a refined version of an earlier approach (introduced in the seminal work of Gao et al.) which enforces constant plus proportional decrease rate of change of the sliding variable. In our method, the proportional term is modified, so that the rate is always bounded and decreases slower for smaller values of the sliding variable than in the original approach. The refined reaching law proposed in this brief, on the one hand, ensures faster convergence and better robustness of the controlled plant than the earlier approach, and on the other hand, it helps satisfy constraints of important signals in the system. Furthermore, in the latter part of this brief a new nonswitching type reaching law is introduced, and it is demonstrated that it results in further improvement of the system robustness without increasing the magnitude of the critical signals in the system.

LQ optimal and reaching law-based sliding modes for inventory management systems

In this article, the theory of discrete sliding-mode control is used to design new supply strategies for periodic-review inventory systems. In the considered systems, the stock used to fulfil an unknown, time-varying demand can be replenished from a single supply source or from multiple suppliers procuring orders with different delays. The proposed strategies guarantee that demand is always entirely satisfied from the on-hand stock (yielding the maximum service level), and the warehouse capacity is not exceeded (which eliminates the cost of emergency storage). In contrast to the classical, stochastic approaches, in this article, we focus on optimising the inventory system dynamics. The parameters of the first control strategy are selected by minimising a quadratic cost functional. Next, it is shown how the system dynamical performance can be improved by applying the concept of a reaching law with the appropriately adjusted reaching phase. The stable, nonoscillatory behaviour of the closed-loop system is demonstrated and the properties of the designed controllers are discussed and strictly proved.

Sliding Mode Dead-Beat Control of Perishable Inventory Systems With Multiple Suppliers

In this paper, we apply control-theoretic approach to the design of inventory policy for systems with perishable goods. In the considered systems, the stock used to fulfill unknown, variable demand is subject to exponential decay. It is replenished from multiple supply sources characterized by different lead times. The challenge is to achieve high demand satisfaction with minimum costs when replenishment orders are realized with non-negligible delay. In contrast to the classical stochastic, or heuristic approaches, a formal design methodology based on discrete time sliding mode (DSM) control is employed. The proposed DSM controller with the sliding plane selected for a dead-beat scheme ensures full demand satisfaction for arbitrary bounded demand. It achieves a given service level with smaller holding costs and reduced order-to-demand variance ratio as compared to the classical order-up-to policy.