Distributed Control for Uncertain Multiagent Systems With the Powers of Positive-Odd Numbers: A Low-Complexity Design Approach

This work shows that low-complexity prescribed performance control (PPC) can be used to realize leader-following consensus for uncertain second-order multi-agent systems (MASs) with the powers of positive odd numbers, i.e., agents whose dynamics are a chain of integrators with positive odd powers. Low-complexity PPC is a control methodology whose strongest feature is its adaptation-free structural simplicity: uncertainty can be handled without estimation of unknown parameters nor approximation structures (neural networks, fuzzy logic systems, etc.) being involved in the control design. While the state of the art has focused on strict- and pure-feedback MASs, i.e., dynamics including a chain of integrators with powers equal to one: in this note, we show that the same low-complexity can be retained for more general integrator dynamics (with positive-odd-integer powers). To this purpose, several new technical tools are proposed to handle the challenges caused by the presence of high powers in the integrators both in leader and follower agents. A dynamical boiler-turbine units system is used to validate the effectiveness of the theoretical findings.