We describe and evaluate a novel approach to formally verify whether a digital control system meets specifications related to step response parameters. In particular, we obtain a state feedback controller designed for a system represented by a state-space model. Then, we analyze whether its required specifications regarding settling time and maximum overshoot are met, using both open-and closed-loop forms and considering finite-word-length (FWL) effects for the latter. We developed our verification approaches inside DSVerifier, which is a verification tool that employs bounded (and unbounded) model checking based on satisfiability modulo theories. Thus, DSVerifier checks performance requirements of digital control systems considering fragility, such as round-off and numerical quantization errors. Our approaches were also evaluated over a set of standard control-system benchmarks extracted from the control literature. Experimental results show that DSVerifier can check settling time and overshoot in control systems suffering from FWL effects, while other existing approaches routinely ignore those issues. Keywords Formal verification • Digital control systems • Finite word length • Controller fragility 1 Introduction A digital control system consists of sensors, controlled systems, control algorithms, and actuators, which together seek to maintain the behavior of a plant's (controlled system) variables under control, i.e., they ensure the desired transientand steady-state responses (Franklin et al. 1998). The development of digital controllers is a crucial task in control engineering since they are routinely used for many different applications, which range from industrial plants to smart cities.
We describe and evaluate the development of mission planners in intralogistics for a commercial unmanned aerial vehicle equipped with a robotic gripper in an industrial environment, which consists of an input warehouse, production lines, and a product depot. In this particular study, the planner produces the needed commands for carrying out a given mission, which includes the delivery of inputs picked up from the warehouse to the production line until the final product is delivered to the client (product depot). We propose two different approaches for mission planning: in the first approach, a simple heuristic is used to solve the mission problem, where a UAV obtains the needed inputs to produce a product from the warehouse, and then it brings the product to the respective production line and waits to finish its production; in the second approach, a technique with task scheduling (production process) is employed; both approaches follow a set of production rules. In addition, a novel evaluation methodology for mission planner algorithms is proposed in order to verify the cost of both approaches, measure the execution time, and compare those results with the optimum cost obtained with the IBM ILOG CPLEX optimizer.
This work describes an approach for synthesizing state-feedback controllers for discrete-time systems, taking into account performance aspects. The proposed methodology is based on counterexample-guided inductive synthesis (CEGIS), producing safe controllers based on step response performance requirements, such as settling time and maximum-overshoot. Controller candidates are generated through constrained optimization based on genetic algorithms. Each iteration that does not satisfy the initial system requirements is learned as a failed result and then used in another attempt. During the verification phase, it is considered the controller fragility to ensure deployable implementations. Such an approach assists the discrete-time control system design since weaknesses occur during implementation on digital platforms, where systems that meet design requirements are employed. The proposed method is implemented in DSVerifier, a tool that uses bounded (and unbounded) model checking based on satisfiability modulo theories. Experimental results showed that our approach is practical and sound regarding the synthesis of discrete state-feedback control systems that present performance requirements. It considers finite word-length effects, unlike other methods that routinely ignore them.
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