This paper presents the design and stability analysis of a Variable Structure Adaptive Backstepping Controller (VS-ABC) for linear plants with relative degree one, using only input/output measurements. Instead of traditional integral adaptive laws for estimating the plant parameters, switching laws are proposed to increase robustness to parametric uncertainties and disturbances, as well as to improve transient response. Moreover, the controller design is more intuitive when compared with the original adaptive backstepping controller, since the relay amplitudes are related to the plant nominal parameters and their respective uncertainties. Simplified algorithm versions are also presented, named Compact and Relay VS-ABC, which reduce the practical implementation complexity, and encourage applications in industrial environments.

This work proposes a control structure to be applied to robotic manipulators, which are articulated mechanical systems composed of links connected by joints. The proposed controller can be divided into two parts. The first one is a left inverse system, which is used to decouple the dynamic behavior of the joints. The second is a sliding mode controller, which is applied for each decoupled joint. It is important to note that the proposed structure, using only input/output measurements, reduces the control signal 'chattering', and it is robust to parametric uncertainties. Besides all the characteristics presented, the proposed structure simplifies the design of sliding mode controller to be applied in robotic manipulators. All these features are verified by simulations.

On March 11, 2020, the world health organization (WHO) characterized COVID-19 as a pandemic. When the COVID-19 outbreak began to spread, there was no vaccination and no treatment. To epidemic diseases without vaccines or other pharmaceutical intervention, the only way to control them is a sustained physical distancing. In this work, we propose a simple control law to keep the epidemic outbreak controlled. A sustained physical distancing level is adjusted to guarantee the fastest way to finish the outbreak with the number of hospitalized individuals below the desired value. This technique can reduce the economic problems of social distancing and keeps the health care system working. The proposed controller is a closed-loop approach that uses the number of hospitalized individuals as the feedback signal. It also does not need massive swab tests, which simplify the application of the technique. We do stability analyses of the proposed controller to prove the robustness to uncertainties in the parameters and unmodeled dynamics. We present a version of the proposed controller to operate using steps to reopen, which is relevant to help the decision-makers. The proposed controller is so simple that we can use a spreadsheet to calculate the physical distancing level. In the end, we present a set of numerical simulations to highlight the behavior of the number of hospitalized individuals during an epidemic disease when using the proposed control law. We simulate the proposed controller applied to the ideal case, considering uncertainties, unmodeled dynamics, a 10 days latent period, and different values of the desired number of hospitalized individuals. In all cases, the proposed controller ensures the number of hospitalized individuals lower than the upper limit of a predefined range.

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