Digital-to-analog converters (DACs) are used to reconstruct digital quantised signals in the analog domain. Practical DACs exhibit several non-ideal effects e.g., principally integral non-linearity (INL). INL is caused by element mismatch, meaning actual output levels deviate from ideal counterparts causing signal distortion. To reduce this error a method employing moving horizon optimal control is proposed where INL has been integrated into the model. The model is built by precisely measuring the INL of the physical device and organising the data into a lookup table. Previous attempts at using moving horizon optimal quantiser (MHOQ) have assumed ideal quantisation, and are therefore unable to reduce the impact of INL. Several other methods exist that can linearise and mitigate the impact of INL but have significant drawbacks such as lack of guaranteed stability, complexity, and the need to use specialised and custom circuit topologies that cannot be replicated with off-the-shelf equipment. The effectiveness of the proposed method is demonstrated via simulations as well as experiments on a common off- the-shelf DAC. Keywords: Digital-to-analogue converters, predictive control, quantisation, signal processing, moving horizon, constrained set 1. INTRODUCTION In a typical digital signal processing system an analog- to-digital converter (ADC) performs sampling and quanti- sation to obtain a digital representation of a signal and a digital-to-analog converter (DAC) is used to recreate the sampled and quantised signal in a physical form, typically a current or voltage. DACs are key to bridging the analog and digital domains. Higher accuracy and res- olution from DACs are called for in applications such as digital audio and video recording (Goedhart et al., 1982), adaptive optics (Beckers, 1993), interferometry (Abbott et al., 2009), scanning probe microscopy (Fantner et al., 2005), systems for lithography (Biswas et al., 2012), and metrology (Hamilton and Tang, 1999). To meet the in- creasing requirements posed by precision applications, it is desirable to improve DAC performance. The use of a DAC introduces several non-ideal effects into a system, causing unwanted noise and disturbance. The principal source of these effects in modern high-resolution DACs is non-linearity due to element mismatch (Galton, 2010) — described using a static non-linear function called the integral non-linearity (INL). A static non-linearity will generate harmonic distortion if it is excited by a sinusoidal signal (Bussgang et al., 1974). Several methods exist to mitigate INL; component se- lection (Zander, 1971), physical calibration (Groeneveld et al., 1989), special layout techniques, laser trimming, ⋆This work was supported by the Research Council of Norway, project FRIPRO 313716.and distributed biasing (Andersson et al., 2003). However, these methods can not address matching errors that re- main after fabrication. To address matching errors, dy- namic methods that manipulate the input signal or circuit elements using digital circuitry are employed; dynamic element matching (DEM) (van de Plassche, 1976; Gal- ton, 2010), periodic high-frequency dithering (Eielsen and Fleming, 2017), large high-pass noise dithering (Leyon- hjelm et al., 1998) and noise-shaping with digital cali- bration (Frey and Loeliger, 2007). For a comprehensive overview of existing techniques aimed at improving DAC accuracy, refer to Eielsen and Fleming (2017) and the